Pat chicken dry and pound to even thickness. Season with salt, pepper, garlic powder, and paprika.
Heat olive oil in a large skillet over medium heat. Cook chicken 5–6 minutes per side until golden and cooked through. Remove and set aside.
In the same skillet, melt butter. Add mushrooms and cook until softened and lightly browned. Remove and set aside.
Add onions to the skillet and cook over medium-low heat until soft and caramelized.
Return chicken to the skillet. Top with mushrooms, onions, and shredded cheese.
Cover skillet and cook on low until cheese is fully melted and bubbly.
Remove from heat and serve hot.