Transfer the salmon skin-side down to a plate (it will not be cooked through). Melt 2 tablespoons unsalted butter in the pan. Add the mushrooms and sear undisturbed until the bottoms are well-browned, about 3 minutes. Add the garlic, half the thyme leaves, and the remaining 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper. Cook, stirring once or twice, until the mushrooms are browned all over and just tender, about 3 minutes.