Dust the pork chops on both sides with the flour; season with salt and pepper. Heat 2 tablespoons olive oil in a large skillet over high heat. Add the pork chops and cook until golden brown, 4 minutes. Flip; cook until lightly golden on the other side, 2 more minutes. Remove to a plate.
Reduce the heat to medium high; heat the remaining 1 tablespoon olive oil in the skillet. Add the bell peppers, onion, chopped garlic, pepperoncini, 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring occasionally, until the vegetables are softened, 10 minutes. Stir in the pepperoncini brine and chicken broth. Return the pork to the skillet. Reduce the heat to medium low; cook, flipping the pork halfway through, until cooked through and the liquid is reduced, 5 minutes.
Meanwhile, preheat the broiler. Combine the butter, grated garlic and 1/4 teaspoon salt; spread on the bread. Transfer to a baking sheet and broil until toasted, 1 minute. Slice the bread and sprinkle with the parsley. Serve with the pork chops and vegetables.