Preheat oven to 425 degrees F. Brush a parchment-lined baking sheet with the vegetable oil. Combine the almonds, breadcrumbs, salt, pepper, and cayenne in a sided dish.
Lightly brush the fillets all over with the mayonnaise. Coat each fillet in the almond mixture, gently pressing it on to help it adhere and then place on the baking sheet. Bake for 8 to 10 minutes, or until cooked through.