In a large heatproof bowl or pot, combine 1 cup kosher salt and 1/2 cup sugar with 4 cups warm water. Stir until dissolved. Add smashed garlic, thyme sprigs, peppercorns and bay leaves. Add 4 cups cold water to cool the brine to near room temperature.

Brine the chicken

Submerge the whole chicken in the brine, breast side down. If needed, weigh the chicken with a plate to keep submerged. Refrigerate for 4 to 6 hours (up to 8 hours for more flavor).

Preheat and prep

When brining is finished, preheat oven to 425°F (220°C). Remove chicken from brine, discard brine, and pat the bird thoroughly dry inside and out with paper towels. Place in a bowl with ice or run cold water through cavity briefly if you need to chill faster; then dry. Rub softened butter under and over the skin (reserve a little for finishing). Rub olive oil on skin, then sprinkle 1 tsp salt and 1/2 tsp freshly ground black pepper evenly over the exterior.

Truss and roast

Arrange carrots, onion quarters and celery in the bottom of a roasting pan to form a vegetable bed. Place the chicken breast-side up on top of the vegetables, tucking wing tips under and tying legs if desired. Roast in the preheated oven at 425°F (220°C) for 15 minutes to develop color, then reduce oven temperature to 375°F (190°C) and continue roasting until an instant-read thermometer inserted into the thickest part of the thigh (avoiding bone) registers 160–162°F (71–72°C), about 40–55 more minutes depending on bird size.

Rest the chicken

Remove chicken from oven and transfer to a cutting board. Tent loosely with foil and rest for 15–20 minutes (the internal temperature will rise to about 165°F / 74°C). While the chicken rests, proceed to make the pan sauce.

Vegetable Bed & Pan Sauce

Roast vegetables

While the chicken roasts, toss the carrots, onion and celery with 1 tablespoon olive oil and a pinch of salt and pepper. They will roast beneath the chicken and pick up drippings; if vegetables are done early, remove and keep warm.

Deglaze the pan

After removing the chicken, place the roasting pan over two burners set to medium (if using a stove-safe pan) or transfer vegetables and pan juices to a large sauté pan. Add 1/2 cup dry white wine or 1/2 cup chicken stock to deglaze, scraping up browned bits with a wooden spoon. Reduce by half, about 2–3 minutes.

Make the sauce

Add 1 cup low-sodium chicken stock to the pan and simmer 4–5 minutes to concentrate flavors. Strain the pan juices through a fine-mesh sieve into a small saucepan, pressing on solids to extract flavor. Return strained liquid to medium heat and whisk in cold butter, 1 tablespoon at a time, until the sauce is glossy and slightly thickened. Taste and adjust seasoning with salt and pepper as needed.

Carve and serve

Carve the rested chicken into breasts, thighs, drumsticks and wings. Spoon some pan sauce over the carved pieces and arrange on a platter with roasted vegetables. Garnish with chopped parsley and lemon wedges if using.

Garnish (optional)

Sprinkle chopped fresh parsley over the plated chicken and serve with lemon wedges for squeezing.