1 stem rosemary

1 bay leaf

4 medium cloves garlic, crushed

1/3 cup low-sodium or homemade chicken broth, or more as needed

Juice from half a medium lemon (about 1 tablespoon) plus more as needed

1 teaspoon cornstarch

1 tablespoon cold water

Chopped chives or flat-leaf parsley, for garnish

1. Preheat the oven to 250 degrees. Thoroughly rinse the chicken, especially the cavity, in cold water; pat dry with paper towels. Season the bird all over with lots of salt and pepper. Bend the wingtips back and tuck under the bird.

2. Heat the oil in a medium Dutch oven or casserole over medium-high heat until the oil starts to shimmer. Add the bird, breast side down; sear undisturbed for 5 minutes. If the chicken doesn't release easily from the pot, sear for 1 to 2 minutes more. Use tongs to turn the chicken over, making sure the wings stay tucked underneath.

3. Add the vegetables, arranging them around the chicken. Cook for 5 to 6 minutes; stir and add the herbs and garlic, along with the neck and liver, if desired (for flavor).

4. Press a large piece of aluminum foil directly onto the chicken (molding it to the bird), with the excess foil draped over the side of the pot. Cover with the lid and bake for 50 minutes, until the internal temperature of the thigh registers 155 degrees on an instant-read thermometer. (Residual heat will cause the temperature to rise by as much as 10 degrees.)

5. Let the chicken rest for 20 minutes, with the lid off and the foil loosened. Transfer the chicken to a cutting board; first drain any juices into the pot. The chicken will be slightly browned, with skin that is more soft than crisp.

6. Use a carving knife to cut the chicken into 10 pieces: the wings (with tips trimmed off); legs; thighs, and the breast sides cut off the carcass and halved. Place in an ovenproof dish, tent loosely with foil and keep warm in the turned-off oven while you prepare the sauce.

7. Set a strainer over a large fat-separator cup. (Discard the bay leaf, herb sprigs and the neck, liver, etc., if used.) Use a wooden spoon to dislodge any brown bits from the bottom of the pot, then strain the contents into the cup, pressing the vegetables with the spoon to extract as much juice as possible; discard the solids.

8. Discard the separated fat. Pour the rich chicken juices into a separate liquid measuring cup; there should be about 2/3 cup. Add enough chicken broth to total 1 cup; pour into a small saucepan. Add the lemon juice and bring to a boil over medium-high heat.

9. Combine the cornstarch and water in a small bowl to form a slurry. Whisk into the saucepan, stirring for 30 seconds or until a sauce forms that is just thick enough to coat the back of a spoon. Season with salt and pepper.