Get out and measure your ingredients.
Place butter in an oven-safe skillet over medium high heat.
Wait until melted.
Add onions.
Stir while cooking, about 15 minutes until softened and tender.
Remove onions from skillet and set them aside.
Turn oven on to 350 degrees.
Coat chicken breasts with olive oil and season with salt, pepper, and dried thyme leaves. Cook chicken in skillet for about 5 minutes per side.
Move chicken to a plate and cover with a paper towel or aluminum foil.
Return onions to skillet.
Sprinkle with flour.
Stir and cook for about 1 minute or two.
Pour in beef broth.
Stir until thickened.
Add chicken back to skillet and spoon sauce over the chicken.
Top with one slice of mozzarella or provolone and one slice of swiss on each breast.
Move skillet to a 350 degree oven and bake until cheese is melted and chicken is cooked through, about 8 to 10 more minutes.
Remove from oven and spoon more of the sauce over the chicken.
Top with fresh parsley, if desired, and serve hot with mashed potatoes or rice.