Season pork chops with salt and pepper. Let them come to room temperature.
Preheat the oven to 400F degrees. Place cast iron skillet in oven.
Heat the butter in a saucepan over medium heat and add the onions. Cook (stirring periodically) until the onions are golden brown and starting to caramelize, about 15-20 minutes.
While the onions cook, remove the heated cast iron skillet from oven and place over medium high heat.
Add the pork chops and sear until golden brown (about 2-3 minutes per side, depending on thickness).
Add the sherry, broth and thyme to the pan. Top with caramelized onions.
Place in the oven and cook for about 5-7 minutes. The internal temperature should be about 145 degrees.
Remove from oven and turn the broiler on.
Lay 1-2 slices of cheese over each pork chop.
Place under the broiler for 1-2 minutes, or until cheese starts the lightly brown.
Drizzle sauce over the pork chops and serve immediately.
Notes
If you don't have a cast iron skillet, heat a regular skillet over high heat and sear the pork chops according to the instructions. Add the sherry and let it burn off for about 20 seconds. Remove chops to an oven proof dish and add the beef broth and thyme. Follow remaining instructions to cook pork chops.