INGREDIENTS

For the chicken:
    1 (4- to 5-pound) whole chicken, neck and giblets removed from the cavity
    Kosher salt
    Freshly ground black pepper
    1 medium lemon, cut into 8 wedges
    2 (7-inch) rosemary sprigs
    1/4 cup olive oil
    4 tablespoons unsalted butter (1/2 stick)
    1/2 teaspoon soy sauce
    4 medium garlic cloves, smashed

For the sauce:

    2 tablespoons unsalted butter
    2 tablespoons finely chopped shallot
    1/3 cup dry white vermouth
    3 tablespoons all-purpose flour
    2 cups low-sodium chicken broth or stock
    Kosher salt
    Freshly ground black pepper

INSTRUCTIONS

For the chicken:

1. Place the chicken on a work surface or cutting board and pat it dry with paper towels. Season generously inside and out with salt and pepper. Cover and refrigerate for at least 1 hour, or preferably overnight.Heat the oven to 375°F and arrange a rack in the middle.
   
   
2. Remove the chicken from the refrigerator and let it sit at room temperature.Fill a small saucepan halfway with water, add the lemon wedges, and bring to a boil over high heat. Reduce the heat to medium and simmer until the rinds are very soft, about 10 minutes. Drain and set aside.Meanwhile, place a small strainer over a medium bowl and set aside.
3. Remove the leaves from 1 of the rosemary sprigs and discard the stem; you should have about 1 tablespoon of leaves.
4. Heat the olive oil, butter, soy sauce, garlic, and rosemary leaves in a medium frying pan over medium heat, stirring often until the garlic is golden and the rosemary is crispy, about 4 minutes.
5. Strain the butter mixture. Remove the garlic and set it aside, reserve the rosemary leaves for the sauce, and reserve the butter-oil mixture for basting the chicken. Wipe out the pan with a paper towel and set it aside.Pat the chicken dry with paper towels.
6. Place 6 of the lemon wedges, the remaining sprig of rosemary, and the reserved garlic in the cavity. Place the chicken in the reserved frying pan and brush it with some of the reserved butter-oil mixture.
7. Place in the oven and roast, basting every 15 minutes, until the skin is browned, the juices run clear, and a thermometer inserted into the inner thigh (but not touching the bone) registers 165°F, about 60 to 75 minutes. Discard any remaining butter-oil mixture.

For the sauce:

1. When the chicken is done, transfer it to a cutting board, tipping the chicken as you remove it from the pan to let the juices from the cavity drip back into the pan. Cover the chicken with a piece of aluminum foil. Finely chop the remaining 2 lemon wedges, and, using your fingers, crumble the reserved rosemary leaves; set both aside separately.
2. Pour the drippings from the roasted chicken into a medium heatproof bowl. Let sit for a few minutes for the fat to rise to the top, then skim the fat off with a spoon and discard (alternatively, use a fat separator); set the drippings aside.
3. Place the frying pan over medium heat and add the butter. When it foams, add the shallot and cook, stirring occasionally, until softened, about 3 minutes. Add the vermouth and reserved chopped lemon and let cook, scraping up any browned bits from the bottom of the pan with a wooden spoon, until the vermouth is reduced by half, about 3 minutes.
4. Add the flour and cook, stirring constantly, until the raw taste has cooked off, about 2 minutes. Slowly whisk in the broth or stock, whisking out any lumps. Add the reserved drippings and crumbled rosemary. Bring the sauce to a simmer and let cook until thickened and slightly reduced, about 10 minutes. Taste and season with salt and pepper.