First, preheat the oven to 375°F (190°C). Dry the chicken breasts with a paper towel so the seasoning sticks better. Season both sides generously with salt, pepper, and dried thyme.
Heat olive oil in a skillet and add the sliced mushrooms. Let them cook until they release moisture and turn golden. Add the garlic and stir for about a minute until fragrant.
Spread half the mushroom mixture in a baking dish. Lay the seasoned chicken breasts on top, then spoon the remaining mushrooms over them. Sprinkle mozzarella and Parmesan evenly. Bake for 25–30 minutes, until the cheese is melted and bubbly and the chicken reaches 165°F (74°C). Rest for 5 minutes before serving.