1 (3 1/2-pound) chicken, cut into 8 pieces (or use 3 1/2 pounds bone-in chicken parts)
2 teaspoons kosher salt (Diamond Crystal), plus more as needed
1 teaspoon freshly ground black pepper, plus more as needed
4 garlic cloves
2 tablespoon extra-virgin olive oil, plus more as needed
2 tablespoons unsalted butter
1 cup thinly sliced mushrooms (preferably specialty mushrooms, such as king, hen-of-the-woods, chanterelles or black trumpet, or a combination)
2 large leeks (4 cups), halved and thinly sliced into half-moons (use white and light green parts)
2 to 3 rosemary sprigs
1 cup dry white wine (or use a dry red or ros
1 cup creme fraichi, plus more for serving if desired
2 tablespoons chopped chives
1 teaspoon finely grated lemon zest, plus more for serving
1 cup finely chopped fresh parsley, leaves and tender stems
Pat chicken dry with paper towels. Season all over with 1 1/2 teaspoons salt and the black pepper. Finely grate, pass through a press or mince 2 garlic cloves. Set aside half the grated garlic for finishing the dish. Rub the rest all over the chicken pieces. Set aside the chicken while preparing the other ingredients.
In a Dutch oven over medium-high heat, combine 1 tablespoon oil and 1 tablespoon butter. When the butter melts, add chicken in batches and cook until browned on both sides, 4 to 6 minutes per side. If the pan dries out, add a little more oil as needed. Transfer browned chicken to a plate.
Add remaining tablespoon each oil and butter to the pan. Once the butter melts, add mushrooms and cook undisturbed until well browned on one side, 2 to 3 minutes. Stir and cook for 1 minute longer.
Thinly slice 2 garlic cloves. Reduce heat to medium, and stir in sliced garlic, leeks and a large pinch each of salt and pepper. Cook, stirring occasionally, until leeks are tender and golden brown, 7 minutes. Add rosemary and wine to the pot and let simmer, scraping up the browned bits, until liquid reduces by half, about 1 minute.
Nestle chicken, skin side up, into the pan and pour in any accumulated juices from the plate. Reduce heat to medium-low and cook, covered, until chicken is cooked through, 25 to 35 minutes.