Preheat oven to 425°F with rack in upper third.
Toss halved carrots with 2 tablespoons melted butter, 1 tablespoon oil, 1 teaspoon salt and ½ teaspoon pepper in a 9-by-13-inch metal baking pan (do not use glass, which could shatter); spread in a single layer.
Roast, flipping halfway through, until browned and tender, 35 to 40 minutes.
Whisk ½ cup broth, 1 tablespoon lemon juice, the grated garlic and the remaining 2 tablespoons butter in a small bowl.
Carefully pour into the pan; roast until the liquid is reduced by half, about 8 minutes.
Sprinkle with 1 teaspoon thyme.
