Lay chicken out on a clean surface. Cover chicken with plastic wrap and pound to an even thickness. Season chicken with salt and pepper.
In a large, oven-proof pan, over medium-high heat, add olive oil. Saute each side of the chicken breasts 3-4 minutes until browned on both sides. Transfer to a plate.
In the same pan, melt butter over medium-low heat. Add onions and saute for 15 minutes until caramelized, stirring occasionally.
Sprinkle flour over the onions, continue to saute for 2 more minutes. Add beef broth, salt, pepper, and Italian seasoning to the pan and stir to combine. Bring to a boil. Add the chicken back to the pan and spoon the onion broth over the chicken. Place into oven and bake for 15 minutes. Remove from oven, place 2 slices of cheese over each chicken, and place back into the oven for the cheese to melt. Bake for 10 more minutes.
Spoon onion broth over the chicken. Garnish with parsley or thyme.
Notes
If you do not have an oven-safe pan, you may use an oven-safe baking pan instead. Follow the recipe and assemble sauteed onions then chicken in the casserole dish. Then, follow the baking directions.