8 small bone-in, skin-on chicken thighs (4 to 5 oz. each), trimmed of excess skin and fat
Kosher salt and freshly ground black pepper
2 tsp. vegetable oil
2 medium shallots, minced
1-1/2 tsp. all-purpose flour
1 cup amber lager, such as Dos Equis Ambar
1/2 cup lower-salt chicken broth
1-1/2 Tbs. pure maple syrup
1/2 tsp. chopped fresh thyme; more for garnish
1 Tbs. whole-grain mustard
1 oz. (2 Tbs.) unsalted butter
Position a rack in the lower third of the oven, set a large rimmed baking sheet on the rack, and heat the oven to 475°F. Season the chicken thighs all over with salt and pepper.
Heat the oil in a heavy-duty ovenproof 12-inch skillet over medium-high heat until shimmering hot. Swirl to coat the pan bottom. Arrange the chicken in the pan skin side down in a single layer (it will likely be a snug fit), cover with an ovenproof splatter screen (if you have one) and cook until the skin is deep golden-brown, about 7 minutes. Turn the thighs and transfer the skillet and splatter screen, if using, to the oven. Roast until an instant-read thermometer inserted into the thickest part of a thigh registers 170°F, 5 to 8 minutes. Transfer to a plate.
Pour off all but 1 Tbs. fat from the skillet. Add the shallots and sauté over medium heat until softened, about 2 minutes. Stir in the flour until combined. Stir in the beer, chicken broth, maple syrup, and thyme. Increase the heat to high and bring to a boil, scraping up any browned bits from the skillet with a wooden spoon. Simmer vigorously until reduced to about 1 cup, about 3 minutes. Remove from the heat and whisk in the mustard, then the butter. Season the sauce to taste with salt and pepper.
To serve, dip each chicken thigh in the sauce and turn to coat. Arrange 2 thighs on each of 4 plates, spoon additional sauce over them, and garnish with the thyme. Serve immediately.