Spread the oil on a baking sheet and position on a rack in the upper third of the oven; preheat to 450 degrees .
In a large bowl, combine the panko, salt and cayenne. In another bowl, beat the eggs. Coat the fish with the seasoned panko, dip in the beaten eggs, then recoat with the panko; transfer to a plate.
Arrange the fish on the preheated pan and bake, turning once, until just cooked through, about 10 minutes.