Season the chicken breasts generously on both sides with salt and pepper. Let them rest for about 5 minutes before cooking.

Heat the olive oil in a large skillet over medium-high heat until shimmering. Cook the chicken for 7 to 8 minutes per side until golden brown and cooked through to an internal temperature of 165 degrees F. Remove and set aside on a plate.

Cook the bacon in the same skillet over medium heat until crispy. Remove to a paper-towel-lined plate and crumble once cool. Drain all but about 1 tablespoon of bacon grease from the pan.

Add the sliced mushrooms to the skillet with the reserved bacon grease and saute over medium heat for about 5 minutes, stirring occasionally, until tender and lightly browned. Do not crowd the mushrooms.

Pour in the chicken broth and scrape the bottom of the pan firmly to deglaze. Add the heavy cream and garlic powder, stir to combine, and bring to a gentle simmer.

Cook the sauce for 2 to 3 minutes, stirring occasionally, until it thickens enough to coat the back of a spoon.

Return the chicken breasts to the skillet. Spoon the mushroom cream sauce over each piece, then top with the shredded Monterey Jack and Cheddar cheeses.

Cover and cook over low heat for 2 to 3 minutes until the cheese is fully melted and bubbly. Garnish with crumbled bacon and chopped green onions and serve immediately.