Preheat oven to 400°F (200°C) and lightly grease a 9×12-inch baking dish.

In a large skillet, melt butter over medium-high heat. Add sliced onions, salt, pepper, and half the thyme. Cook until softened (5–8 minutes).

Reduce heat to medium. Continue cooking until onions are caramelized and jammy, about 15 minutes. Add ¼ cup of broth if pan gets dry.

Optional: Add balsamic vinegar to deglaze the pan. Let it reduce for 1 minute.

Stir in garlic, cook for 1 minute, then remove from heat.

Cut chicken breasts horizontally to create pockets. Season inside and out with salt, pepper, garlic powder, and ground thyme.

Stuff each chicken breast with caramelized onions, gruyere, and parmesan. Seal with toothpicks.

Transfer remaining onions to the baking dish, mix with remaining ¼ cup broth, and place stuffed chicken on top.

Heat oil in the skillet and sear stuffed chicken breasts 4 minutes per side.

Return chicken to baking dish. Spoon pan juices over chicken, sprinkle remaining thyme, and bake 15–20 minutes until fully cooked.

Remove toothpicks and serve warm with onions and sauce.