Preheat oven to 350.
Pat fillets dry and rub with salt and pepper, to taste.
Dredge fillets in flour and basil mixture.
Add butter and olive oil to a pan over medium high heat.
Place the fillets in the hot pan and sear the fish on both sides, about 3-4 minutes a side.
Remove fish from pan and transfer to a baking dish.
Place fish into oven and bake for 12-15 minutes, depending on the fillets thickness.