Preheat the oven to 400 degrees F.
Heat 2 tablespoons of the oil in a large skillet over medium-high heat. Add the pepper flakes and cook for 30 seconds. Add the sausage and brown, breaking the meat up with a fork, for about 3 minutes. Stir in the sage and cook for 1 minute more. Pour off the fat and transfer the sausage to a bowl. Stir in the peaches, cheese, and pepper.
With a sharp knife, cut a pocket in the side of each chop, slicing horizontally, almost through to the other side. Season with salt and additional pepper, and then stuff the chops generously with the filling.
In a large ovenproof skillet, working in 2 batches if necessary, heat the remaining 4 tablespoons oil until very hot. Sear the chops on one side until browned, 3 to 4 minutes. Turn the chops and transfer the skillet to the oven to finish cooking, 20 to 25 minutes more. Serve immediately, spooning over any stuffing that might fall out.