1. Preheat oven to 375°. Heat olive oil in a large, heavy ovenproof frying pan (not nonstick) over high heat until oil is hot but not smoking. Add chicken breasts, top side down, and cook until golden, 2 to 3 minutes. Turn chicken over.
2. Add shallots and garlic to pan with chicken, stirring occasionally so garlic doesn't burn, until shallots are soft and translucent, 3 to 4 minutes. Add beef broth, thyme sprigs, mushrooms, 1/2 tsp. salt, and 1/4 tsp. pepper and cook until mixture begins to boil, about 1 minute.
3. Cover pan and put in oven. Bake 14 to 16 minutes, or until chicken is just cooked through (cut to check). Transfer chicken to a plate.
4. Season mushroom-broth mixture with salt and pepper to taste. Divide vegetables among 4 rimmed plates or shallow pasta bowls, top each with a piece of chicken, and spoon sauce over all. Garnish with chopped thyme and gruyere.
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