Place the flour in a flat dish and dredge the fish on both sides, shaking off any excess flour.
Heat 2 tablespoons of the butter in a large non-stick pan over medium heat until foaming and lightly browned (careful, butter goes from brown to burnt very quickly).
Working in two batches if necessary, cook the fish, turning once, for about 6 minutes total, until it's nicely browned on both sides and flakes with gentle pressure from your finger. Place a fillet on each of 4 warm plates.
Add the remaining 2 tablespoons butter, the lemon juice and zest, and parsley to the pan.
