Heat 1 tbsp olive oil in a large oven-safe skillet over medium heat. Add onion and cook 2 minutes, then add mushrooms. Cook 5 to 6 minutes until liquid evaporates and mushrooms are golden. Stir in garlic and parsley, cook 1 minute, and season with salt and pepper. Remove from heat to cool slightly.

Pat chicken dry. Cut a horizontal pocket into each breast, leaving a ½-inch border. Season inside and out with salt and pepper.

Mix cooled mushroom mixture with cream cheese and parmesan. Spoon 2 to 3 tbsp filling into each pocket, seal edges gently, and use toothpicks if needed. Wipe skillet, add oil, and heat over medium-high. Sear chicken smooth-side down for 3 to 4 minutes, flip, and sear the other side 3 minutes.

Preheat oven to 400°F (200°C). Transfer chicken to a baking dish if needed, then bake 18 to 20 minutes until a thermometer reads 160°F in the thickest part.

Rest chicken 5 minutes. Remove toothpicks, slice on a slight angle, and spoon any pan juices over the top. Serve warm.