1. To prepare, rinse chickens inside and out and pat dry with paper towels. Sprinkle generously inside and out with salt and pepper. Cover and refrigerate for at least 1 hour, or preferably overnight, before cooking.
2. When chickens are ready, heat the oven to 375°F and arrange the rack in the middle. Fill a small saucepan halfway with water, add lemon wedges, and bring to a boil over medium-high heat. Reduce heat to medium and simmer until rinds are thoroughly softened, about 10 minutes. Drain and reserve 6 wedges for the chicken. Finely chop remaining 2 lemon wedges and reserve separately for the sauce.
3. Strip the leaves from 3 of the rosemary sprigs and discard the stems; you should have about 3 tablespoons of needles. Combine olive oil, butter, soy sauce, garlic, and rosemary needles in a small frying pan and heat over medium heat until butter melts and garlic is golden, about 3 minutes. (The rosemary will turn crispy as it fries in the butter.) Remove the rosemary needles and garlic from the butter, and reserve each separately. Reserve the flavored butter mixture.
4. Remove chickens from the refrigerator and pat dry with paper towels. Fill the cavity of each bird with 3 lemon wedges, 1 of the remaining sprigs of rosemary, and 1/2 of the sautéed garlic. Place birds in a large baking dish or roasting pan. Brush chickens with the flavored butter and roast until the skin is crisp and the meat is thoroughly cooked but still juicy, about 60 to 65 minutes. (An instant-read thermometer inserted into the thickest part of the thigh should read 160°F to 165°F.)

1. Meanwhile, make the sauce: Combine chicken broth and vermouth in a medium saucepan and bring to a boil over medium-high heat. Once mixture boils, reduce heat to medium and simmer until liquid is reduced by about half, 10 to 12 minutes. Reduce heat to low and keep warm. When chickens are done, transfer them to a cutting board, tipping each bird as you remove it to let the juices from the cavity drip back into the pan. Cover birds with a piece of aluminum foil and pour off any excess grease from the pan. Pour hot broth mixture from the saucepan into the baking pan and deglaze, scraping up any browned bits on the bottom with a wooden spoon or spatula. Return mixture to the saucepan and bring to a simmer over medium heat.
2. Meanwhile, melt butter in a small frying pan until foamy. Add shallot, reserved chopped lemon, and reserved rosemary needles and cook, stirring frequently, until browned, about 3 minutes. Sprinkle flour over the mixture and cook, whisking constantly, until the flour is absorbed and looks slightly toasted, about 3 minutes.
3. Carefully add 1/2 cup of hot broth mixture to the frying pan, whisking constantly until completely blended. This will produce a smooth paste that will thicken the sauce. Gradually whisk the paste back into the hot stock, and simmer until the sauce is thickened, 10 to 12 minutes.
4. Let the chickens rest at least 10 minutes before serving. To serve, carve chickens, serve 2 pieces per person, and ladle sauce on top.

Beverage pairing: Tablas Creek Esprit de Beaucastel Blanc, California. This wine, made in the style of white Châteauneuf-du-Pape from France’s Rhône Valley, brings honey, citrus, flowers, and wild herbs to the table—a gorgeous complement to the herby succulence of the chicken.