Preheat oven to 400 F and melt butter in a large skillet over medium-high heat.
Add onions and cook until tender, about 4-5 minutes.
Stir in 1/4 cup beef broth and continue cooking for about 15 minutes, stirring frequently, until onions are caramelized.
Season pork chops with salt, pepper, garlic powder, and dried thyme.
Transfer onions to a plate and cover, making sure to leave any sauce in the skillet.
Turn heat down to medium, drizzle skillet with vegetable oil, and add pork chops.
Let cook for about 4-5 minutes on each side and transfer to a plate.
Add caramelized onions back to the skillet, add flour, and stir.
Let flour cook into the onions for 1-2 minutes and pour in 1 cup beef broth.
Stir and bring to a boil.
Return pork chops to the skillet, spooning sauce over them, and top each pork chop with a slice of cheese and a small handful of shredded Swiss cheese.
Place skillet in the oven and bake for about 10 minutes, until cheese starts to bubble.
Remove from oven and spoon caramelized onions over pork chops.
