Preheat oven to 400 degrees.
Season chops on all sides with salt & pepper.
Heat 2 tbsp butter in skillet. Brown chops 3-4 minutes on each side flipping once. Transfer to plate.
Add the remaining 2 tbsp butter to same skillet, on medium heat, with any fat from the chops. Add onion slices. Season with salt & pepper. Cook until softened and deep golden, 10-15 minutes. Stir often to keep from burning. Stir in garlic when the onions are mostly done to keep them from burning and becoming bitter.
Stir in sherry & thyme to skillet.
Add the broth, stirring to pick up any browned bits from the bottom of the skillet.
Combine the chops and onion mixture in a baking dish. Top the chops evenly with the cheese.
Bake in oven on top rack until chops are cooked through and cheese is melted, about 8-10 minutes. Then switch over to broil and cook until cheese is browned in spots - about 1-2 minutes.