Preheat oven to 375°F (190°C). Pat chicken thighs dry and season with salt and pepper.
Heat olive oil in a skillet over medium-high heat. Sear chicken thighs, skin-side down, for 4-5 minutes until golden. Set aside.
In the same skillet, melt butter and sauté onions, garlic, and mushrooms until softened, about 5 minutes. Stir in thyme, chicken broth, and heavy cream, bringing it to a simmer.
Transfer the creamy mushroom mixture to a baking dish. Place chicken thighs on top, skin-side up, and sprinkle with shredded cheese.
Bake for 25-30 minutes, or until chicken is fully cooked and cheese is bubbling and golden.
Rest for 5 minutes before serving, garnished with extra thyme if desired.