In a food processor, mix rum butter ingredients until well blended.
Spread onto plastic wrap and roll like a sausage, securing ends.
Refrigerate until firm. (Extra can be frozen for future use). Place fillets on a baking sheet.
Cut ΒΌ inch slices of rum butter and place two on top of each fillet.
Broil (one side only) for 4-5 minutes until fish flakes with a fork.
Sprinkle with fresh parsley.
Serve immediately.