Chicken:

In a large skillet or high-sided sauté pan with a lid, heat the oil and butter over medium-high heat until the foam from the butter begins to subside. Season the chicken with salt and pepper, then put in the pan skin-side down. Cook--resisting the urge to repeatedly poke, prod, and look underneath--until it doesn't stick to the pan and is golden brown, about 6 minutes.

Flip the chicken over, reduce the heat to medium, and cover the pan. Cook until just cooked through, 10 to 15 minutes more. (If you're using both dark and white meat, note that the white meat will cook faster.) Transfer to a platter. If you're making one of the pan sauces, tent the chicken with foil to keep warm and continue with that recipe. If not, sprinkle the chicken with a little salt, and serve hot, warm, or cold.

Garlic Cream Pan Sauce:

Pour off all but about 1 tablespoon of the fat from the pan of sautéed chicken, then return the pan to medium heat. Add the garlic and cook, stirring often, until fragrant, about 1 minute. Add the thyme and stir briefly. Add the wine, scraping up  any caramelized bits from the bottom of the pan, and simmer until most of the wine has evaporated.

Add the cream and any juices accumulated on the platter and simmer until the sauce has reduced slightly and the flavor has concentrated, about 3 minutes. Check the seasonings, adding salt and/or pepper, to taste. Serve the chicken topped with the sauce.

Tomato Fondue Pan Sauce:

Pour off all but about 1 tablespoon of the fat from the pan of sautéed chicken, then return the pan to medium heat. Add the shallots and cook, stirring often, until fragrant, about 1 minute. Add the wine, scraping up any caramelized bits from the bottom of the pan, and simmer until most of the wine has evaporated.

Add the tomatoes and any chicken juices accumulated on the platter and cook, stirring often, until they are slightly broken down and heated through, about 2 minutes. If using cherry tomatoes, gently press them with the back of a spoon.

Off the heat, add the herbs, then swirl in the butter. Check the seasonings, adding salt and/or pepper, if needed. Serve the chicken topped with the sauce.

Lemon-Rosemary Pan Sauce:

Pour off all but about 1 tablespoon of the fat from the pan of sautéed chicken, then return the pan to medium heat. Add the garlic and cook, stirring often, until fragrant, about 30 seconds. Add the rosemary and pepper flakes (if using) and stir briefly. Add the wine, scraping up any caramelized bits from the bottom of the pan, and simmer until most of the wine has evaporated.

Add the broth and any chicken juices accumulated on the platter and simmer until the sauce has reduced slightly and the flavor has concentrated, about 3 minutes. Off the heat, add the lemon juice, then swirl in the butter. Check the seasonings, adding salt and/or pepper, if needed. Serve the chicken topped with the sauce.