Place chicken breasts between two pieces of plastic wrap or parchment paper. Using a meat mallet or heavy pan, pound to an even 1/2-inch thickness. Season both sides generously with garlic powder, onion powder, salt, and black pepper.

In a large oven-safe skillet, melt 1 tablespoon of butter over medium heat. Add sliced onions and mushrooms. Cook, stirring occasionally, for 8-10 minutes until onions are golden brown and caramelized and mushrooms are tender. Remove from skillet and set aside.

In the same skillet, heat olive oil and remaining tablespoon of butter over medium-high heat until butter melts and shimmers. Add chicken breasts and sear for 5-6 minutes per side until golden brown and internal temperature reaches 165°F.

Turn oven to Broil and position rack about 6 inches from heating element. Top each chicken breast with a generous portion of the sautéed mushroom and onion mixture.

Cover the mushrooms and onions with a heavy layer of Monterey Jack cheese, using about 1/2 cup per breast.

Place skillet under broiler for 2-3 minutes, watching closely, until cheese is melted, bubbly, and just starting to develop light golden-brown spots.

Remove from oven and let rest 2-3 minutes. If using brown gravy, warm according to package directions and pour over the top before serving.