Put the flour, salt, and pepper in a pie pan or other flat dish and mix well. Put the milk in another.

Heat 1 Tbs oil and 1 Tbs butter in a frying pan over medium heat. Dip the fish into the milk, then into the flour, then lay it in the frying pan. Do as many pieces of fish as you can fit in your pan. Saute for 2 minutes per side, then remove to a serving dish. If you're doing it in batches, add more oil and butter for the second batch.

When you're done cooking the fish, add the other 2 Tbs butter and cook for a minute or two, stirring constantly, over medium heat until browned. Watch it carefully because you don't want to burn it. Stir in the parsley, lemon juice, and capers and heat for 10-15 seconds, then spoon over the fish.