Pound chicken breasts to an even thickness of approximately 0.5 inches.
Season chicken on both sides with salt, pepper, garlic powder, and onion powder.
Heat 1 tablespoon of olive oil and 1 tablespoon of butter in a large skillet over medium-high heat.
Add sliced onions and mushrooms to the skillet and sauté for 8 to 10 minutes until caramelized and tender. Remove from skillet and set aside.
In the same skillet, add the remaining olive oil and sear chicken for 5 to 7 minutes per side until the internal temperature reaches 165 degrees Fahrenheit.
Top each chicken breast with an equal portion of the sautéed mushroom and onion mixture.
Sprinkle Monterey Jack cheese evenly over the vegetables on each breast.
Cover the skillet with a lid for 1 to 2 minutes until the cheese is fully melted.
Remove from heat and serve immediately.