Preheat your grill or a large skillet over medium-high heat.
In a small bowl, mix olive oil, paprika, garlic powder, onion powder, salt, and pepper.
Coat the chicken breasts evenly with the spice mixture.
Grill or pan-sear the chicken for 6-8 minutes per side, or until cooked through and no longer pink in the center. Remove chicken from the skillet and set aside.
In the same skillet, melt the butter over medium heat.
Add the sliced mushrooms and onions. Cook, stirring occasionally, until softened and lightly browned, about 5-7 minutes.
Pour in the chicken broth and scrape up any browned bits from the bottom of the skillet. Let it simmer for 2 minutes.
Return the chicken breasts to the skillet. Spoon the mushroom and onion mixture over the chicken.
Top each chicken breast with Monterey Jack cheese. Cover the skillet and cook for 2-3 minutes, or until the cheese is melted and bubbly.
Serve immediately.
Notes
For a skillet-only method, you can sear the chicken in the skillet first, remove it, then cook the vegetables in the same skillet before returning the chicken.
Feel free to add a splash of heavy cream to the mushroom and onion mixture for a richer sauce.
Other cheeses like cheddar or pepper jack can be substituted for Monterey Jack.