Step 1
Whisk together the flour and 1/4 teaspoon each salt and pepper in a shallow plate. Coat the fish on one side only. Shake off excess flour and transfer fish flour-side up to a sheet pan or cutting board.
Step 2
Heat 1 tablespoon of the oil in a large stainless steel or well-seasoned cast iron skillet over high heat until just smoking. Add as much sole as will fit comfortably in a single layer, flour side down and cook until bottom is browned, about 2 minutes. With two spatulas, turn the fish and remove pan from the heat. Let stand until just cooked through, about 30 seconds to 1 minute longer. Remove fish to a platter, cover to keep warm and wipe out the skillet. Repeat with the remaining oil and fish. Wipe out the skillet to make the sauce.
Step 3
Heat the butter over medium high heat in the same skillet, swirling the skillet until the butter is lightly browned and smells nutty, about 3-4 minutes.
Step 4
Stir in 1 teaspoon black pepper and the tomatoes and cook 1 minute longer or until the tomatoes are just softened. Season with salt and spoon over the fish. Serve with lemon wedges.
