Combine all dry ingredients. Coat fillets evenly and shake off excess coating.
Heat 1 tablespoon each of the butter and oil over medium-high heat in a large
skillet until butter foams but doesn't burn.
Cook 2 fillets, rounded side down, for 2 minutes. Transfer to a baking sheet,
rounded side up. Wipe skillet, add remaining butter and oil. Repeat cooking
process with remaining fillets. Spread fillets with pesto. Bake for 6 to 7 minutes,
or until fish flakes easily when tested with a fork.
Pesto: Combine all ingredients in food processor with metal blade. Pulse-chop
to a coarse paste. Use immediately or cover and refrigerate.