Serves 6 - 8
1 (4- to 5-pound) chicken
1 tablespoon kosher salt
2 medium Meyer or regular lemons
2-1/2 tablespoons olive oil, divided
1-1/2 teaspoons dried thyme
1 pound shallots
1/2 to 3/4 cup chicken broth
1/3 cup dry white wine
Preheat oven to 375°. Zest lemons. Slice 1 lemon; juice half of the other.
Rub zest under as much of the skin as possible and rub any remaining zest inside cavity. Rub chicken all over with 1 tablespoon olive oil and the thyme. Put lemon slices in cavity.
Set a V-shaped rack in a heavy roasting pan large enough to hold shallots. Put chicken in rack, breast side up. Add shallots to pan and drizzle with remaining 1 1/2 tablespoon olive oil, turning them to coat the onions in the oil.
Roast chicken, basting every 30 minutes or so, until browned about 1 1/2 to 1 3/4 hours (remove shallots after 1 hour and set aside). Remove from oven to let it rest before carving.
Meanwhile, make sauce: Pour pan drippings into a measuring cup with a pouring lip. Trim tops from shallots and squeeze soft insides into a blender. Pour off all but about 1 tbsp. fat from pan drippings and add drippings to blender. Add 1/2 cup broth and the wine and pulse until smooth.
Pour sauce into roasting pan. Cook, scraping up brown bits and adding more broth if you want a thinner sauce, over medium-high heat until sauce turns a nutty brown, about 10 minutes. Stir in 1 tablespoon reserved Meyer lemon juice, or more to taste. Carve chicken, serve with sauce.