Preheat oven to 400°F. Carefully slice chicken breasts to create pockets without cutting through completely. Lightly pound with rolling pin to even thickness.
Heat 2 tablespoons olive oil in large skillet over medium-high heat. Add chopped mushrooms and sauté for 5 minutes until browned.
Add diced onion and cook for 3 minutes. Stir in parsley, garlic, thyme, salt, and pepper. Cook 1 more minute until fragrant.
In small bowl, combine mushroom mixture with 1 cup Gouda cheese. Mix well to create filling.
Heat 2 tablespoons olive oil in same skillet over medium-high heat. Sear chicken breasts for 2 minutes per side until golden.
Stuff each chicken breast with mushroom-cheese mixture. Place in baking dish and bake for 50 minutes.
While chicken bakes, heat 1 tablespoon olive oil and cook sliced mushrooms for 2 minutes.
Remove chicken from oven. Top with remaining 1 cup Gouda cheese and sautéed mushrooms. Return to oven for 7-10 minutes until cheese melts.