Preheat the oven to 375°F (190°C).
Combine the flour, black pepper, and cayenne pepper in a large zip-top bag and shake to mix.
Place the beaten egg white in a shallow bowl. Dip each chicken breast in the egg white, letting excess drip off.
Put one egg-coated chicken breast at a time into the flour mixture bag, shake to coat evenly, then remove and set aside. There should be about 3/4 cup flour remaining after coating.
Heat the canola oil in an oven-safe skillet over medium heat. Test the temperature by dropping a pinch of flour in; it should sizzle but not smoke.
Brown the chicken in the skillet about 8 minutes per side until golden.
Leave the browned chicken in the skillet and transfer the skillet to the preheated oven. Bake uncovered for 30 minutes, or until an instant-read thermometer inserted into the thickest part reads 165°F (74°C).
Remove the chicken and place on paper towels to absorb excess oil; note that about half the oil will remain in the skillet.
