Preheat oven to 350°. Line a rimmed baking sheet with foil.
In a shallow bowl, combine flour, salt, and peppers. In a separate shallow bowl, whisk eggs. In a third shallow bowl, place pecans. Dredge each fillet in flour mixture, shaking off excess. Dip fillet in egg, letting excess drip off. Place fillet in pecan mixture, pressing lightly to coat both sides of the fillet.
In a large skillet, melt butter and oil over medium heat. Add fillets, in batches, and cook 2 minutes on each side or until lightly browned. Arrange fillets on baking sheet, and bake 10 minutes or until flesh flakes easily. Serve with Brown Butter Sauce.

Brown Butter Sauce

In a small skillet, combine all ingredients, and cook over medium heat until shallots are tender and butter is browned. Serve warm.