Slice up some zucchini. Sauté it with olive oil and almonds, and top it off with pecorino cheese.

Is this a quick pan-to-fork-to-mouth dish for a weeknight dinner at home? A simple recipe scribbled on the back of an index card at the farmers’ market?

Nope. It’s a specialty at the Red Cat, a smart but cozy restaurant in west Chelsea where the food harks back to a James Dean sort of cool: It looks good without trying too hard. The Red Cat isn’t the sort of place to poach its veal sous-vide or sprinkle cocoa powder all over its chicken — no arty or pretentious touches here. Instead, there are simple ingredients, skillfully combined. And although (or because) it’s an anti-trend restaurant, it boasts a large fan base of locals.

Like its namesake, “The Red Cat Cookbook” (Clarkson Potter, $35) declares its casual appeal right off the bat. “This is not a restaurant cookbook,” the co-owner and co-chef, Jimmy Bradley, who also co-helms the Harrison and the Mermaid Inn, proclaims in the introduction. That’s a bold statement for what is, of course, a restaurant cookbook. But Mr. Bradley speaks the truth on another score. The recipes hardly require the technical wizardry and hours of time that the typical restaurant cookbook demands.

Instead, Mr. Bradley’s recipes have an admirable directness. They manage to excite and soothe at the same time. Tempura green beans with honey-mustard sauce is perfect finger food. The fall squash agnolotti is a savvy combination of winter flavors, combining roasted butternut squash with brussels sprouts, sage, and a bit of Parmesan. It’s a stuffed pasta dish you could actually imagine making on a cold winter’s weeknight. The purée of celery root soup is admirably creamless, allowing the earthy flavor of the celery root to emerge. Main-course pairings are simple and sensible, ranging from pork loin and calf’s liver to shell steaks and leg of lamb.

Though Mr. Bradley insists he’s just a humble Italian-American home cook who also has a fondness for fried clams and goulash, nothing is as simple as it seems. Take that simple sautéed zucchini dish, or, as the Red Cat calls it, the quick sauté of zucchini and almonds. The zucchini is sliced into pretty matchsticks, sautéed in the oil that was just used to toast almonds, and served in a pile flanked by slabs of pecorino. And the Red Cat’s famous simple skillet roast of chicken! By having the butcher bone the chicken so that it can lay flat and sear up crisp in the pan, Mr. Bradley has managed to reinvent the roast-chicken wheel.

Like a consummate host, Mr. Bradley can even make you feel comfortable in unfamiliar surroundings. Many dishes feature unexpected but welcome interplay between sweet, salty, and sour. A risotto flavored with pancetta and peaches sounds wacky, until you think of prosciutto and melon. Salt is also delightfully deployed in a simple roast of button mushrooms and anchovies, as well as a rich seafood sauce for pasta, whose secret ingredient is soy sauce. Sliced heirloom tomatoes are paired with blue cheese puffs rather than straight blue cheese — an ingenious change. Who wouldn’t like their cheese crispy, puffy, and hot instead of lukewarm?

There are only a few bumps in the ride. A dish involving fava beans fails to mention that pre-blanching them makes the peeling go much quicker. And Mr. Bradley writes that he uses cremini mushrooms “to honor [his] New York sensibility” — a puzzling remark.

On the whole, however, “The Red Cat Cookbook” is warm and inviting companion with which to cook through the long winter. And come dessert, you can enjoy a Rocky Road Sundae, as sweet, classic, and cool as the Red Cat itself.

Simple Skillet Roast of Chicken With Fried Tomato Sauce and Polenta

Adapted from “The Red Cat Cookbook” by Jimmy Bradley and Andrew Friedman. For the best presentation (and flavor), get your halved and boned chickens from a butcher, or buy boneless, skin-on chicken parts from the market.

For the chicken:

2 chickens, 3 pounds each, halved and boned, skin on, or 2 to 2 1/2 pounds boneless chicken parts, skin on
Salt and freshly ground black pepper
4 tablespoons canola oil

For the polenta and sauce: 1 1/2 cups low-sodium, store-bought chicken broth
1/2 cup milk
1 tablespoon unsalted butter
2 cups quick-cooking polenta
1/4 cup finely grated Parmigiano-Reggiano Salt and freshly ground black pepper
1/4 cup olive oil
1/2 small onion, finely diced
2 cloves garlic, thinly sliced
1 can (15 ounces) whole peeled tomatoes, crushed by hand, with their juice
1 tablespoon chopped fresh oregano leaves
Pinch of crushed red pepper flakes
1/2 cup parsley leaves
1/2 cup celery leaves

1. Preheat the oven to 450•F. Heat 2 wide, deep, heavy-bottomed ovenproof skillets over high heat. Season the chickens generously with salt and pepper. Add 2 tablespoons of the canola oil to each pan, let it get nice and hot, then put the chicken halves in the pans, skin side down, making sure they lie flat and all skin is in contact with the oil, and cook until the skin is golden, 3 to 5 minutes. Transfer the pans to the oven and roast until the juices from the thickest part of the white meat and the thickest part of the dark meat run clear when the meat is pierced with a sharp, thin-bladed knife, approximately 20 minutes.

2. While the chicken cooks, make the polenta: Put the stock, milk, and butter in a nonreactive saucepan and bring to a simmer over medium heat. Gradually whisk in the polenta and keep whisking until the mixture comes together in a mashed potato-like mass, approximately 8 minutes. Whisk in the cheese and season with salt and pepper. Turn off the heat and cover to keep it warm.

3. Heat the olive oil in a wide, deep, heavy-bottomed sauté pan over high heat. Add the onion and garlic and cook for 1 minute. Add the tomatoes and cook for two minutes, stirring to prevent scorching. Stir in the oregano and red pepper flakes and season with salt and pepper.

4. When the chickens are done, remove them from their pans. Set 1 pan over medium-high heat, add the parsley and celery leaves, and wilt them for 10 seconds. To serve, spoon some sauce into the center of each of 4 dinner plates. Top with some polenta, then a half chicken, then some parsley and celery-leaf salad.

Serves 4.