Pat the chicken breasts completely dry with paper towels. Season both sides generously with salt, pepper, garlic powder, and onion powder.

Heat olive oil in a large oven-safe skillet over medium-high heat until shimmering. Add chicken and cook 6-7 minutes per side until golden brown and internal temperature reaches 165 degrees F. Remove and tent loosely with foil.

Reduce heat to medium. Melt butter in the same skillet, add sliced mushrooms, and cook 5-7 minutes, stirring occasionally, until golden and reduced by about half.

Sprinkle flour evenly over the mushrooms and stir constantly for 1 minute to form a roux.

Gradually whisk in beef broth and milk, scraping up the browned bits from the bottom. Simmer 3-5 minutes, stirring frequently, until gravy thickens enough to coat the back of a spoon. Season with additional salt and pepper to taste.

Return chicken to the skillet. Top each breast with about 1/4 cup shredded Monterey Jack and spoon gravy over and around the chicken.

Place the skillet under a preheated broiler, about 6 inches from the heat source, for 1-2 minutes until cheese is melted, bubbly, and lightly golden. Watch carefully.

Remove from broiler and let the chicken rest 2-3 minutes before cutting. Garnish with crumbled bacon and sliced green onions if desired. Serve immediately.