Melt 3 tablespoons of butter in a large skillet over medium heat. Once foaming, add the thinly sliced onion and a pinch of salt and pepper. Cook for 6-8 minutes, stirring occasionally, until the onions are soft and golden with caramelized edges. This builds a deep, sweet flavor that's essential to the sandwich. Transfer to a plate and set aside.

Pat the pork chops dry with paper towels—this helps them brown better. Season both sides generously with salt, pepper, and garlic powder. Pour the flour into a shallow bowl and coat each pork chop thoroughly on both sides, shaking off excess. Let them sit on a plate for a minute while you heat the oil.

Heat 1/2 cup vegetable oil in a large skillet over medium-high heat until shimmering (about 2-3 minutes). Carefully lay the breaded pork chops in the hot oil and fry for 4-5 minutes on the first side without moving them—this creates a golden, crispy crust. Flip and cook the other side for another 4-5 minutes until the internal temperature reaches 145°F. I like to transfer them to a wire rack immediately after cooking so they stay crispy and any excess oil drains away.

While the pork finishes cooking, lightly toast the potato buns in a dry skillet or toaster until they have a light golden color and extra crunch—this prevents them from getting soggy. Spread about 2 tablespoons of mayonnaise and 2 tablespoons of mustard on the inside of each bun, dividing evenly. Place one warm pork chop on each bun, then top with a generous portion of the caramelized onions from Step 1. Close the sandwiches and serve immediately while everything is still warm.