Step 1

Preheat the oven to 350°F (180°C).

Step 2

In a large, heavy-bottomed pan over medium-high heat, toss in 1 tablespoon butter and 1 tablespoon olive oil and heat until the butter melts. Season the chicken all over with salt and pepper.

Step 3

Working in batches as needed to avoid crowding, add the chicken to the pan, skin side down, and cook, turning once, until golden brown on both sides, about 6 minutes per side.

Step 4

Place the chicken, skin side up, in a roasting pan or a 9-by-13-inch (23-by-33-centimeter) baking dish. Do not wipe the pan clean. Keep the pan with the chicken drippings over medium-high heat.

Step 5

Toss the garlic in the pan and cook, stirring or shaking the pan often, until lightly browned and beginning to soften, 2 to 3 minutes. If you're worried about the garlic scorching, turn down the heat to medium-low. Using a slotted spoon, scatter the garlic evenly over the chicken. Keep the pan over medium-high heat.

Step 6

Add the wine to the hot pan, stirring and scraping up any browned bits on the bottom of the pan, and bring to a simmer. Cook until the liquid reduces by half, about 2 minutes. Add the stock and return to a simmer. Add the remaining 1 tablespoon butter. When the butter has melted, season well with salt and pepper and stir to combine. Carefully pour the sauce all over the chicken and garlic.

Step 7

In a bowl, toss the potatoes with the remaining 1 tablespoon olive oil and season with salt and pepper. Tuck the potatoes in the baking dish all around the chicken. Scatter the thyme sprigs over the top.

Step 8

Roast until the potatoes are fork-tender and the chicken is cooked through (the chicken juices should run clear and no trace of pink should remain when you slice into it), 35 to 55 minutes, depending on the size of your spuds and chicken. If the chicken is done but the potatoes aren't yet sufficiently tender, simply transfer the chicken to a plate, cover loosely with foil, and return the pan with the potatoes to the oven.

Step 9

If desired, skim the fat from the surface of the pan juices. Transfer the chicken and potatoes and garlic cloves to individual plates or a platter, spooning the pan juices over and around the chicken.