Melt 2 tbsp butter into a large cast iron skillet over medium-high heat, and add the porkchops and sear on each side about 4 to 5 minutes. Place the pork chops onto a tray or sheet pan to hold while you make the french onion sauce.
Preheat oven to 350.
In the same skillet as you seared the pork chops, add another 2 tablespoons of butter if needed. Once hot and melted, add the onions, salt and pepper, and allow them to cook down and deeply caramelize for about 15 to 20 minutes, stirring frequently, until the onions become very dark, soft and jammy.
Add in the garlic and thyme, wine, balsamic, and allow it to bubble up and reduce for about 30 seconds. Then pour in the beef stock and whisk or vigorously until smooth. Allow the French onion sauce to simmer to 5 minutes.
Nestle the pork chops into the onion sauce, and top them with some of the onions and shredded cheese. Bake for 20 minutes until cheese is melted and slightly browned.