Rinse the fish fillets and pat them dry with paper towels. Season both sides of the fillets with salt and black pepper.
Set up three shallow bowls on your work surface. In the first bowl, place the flour. In the second bowl, pour the beaten egg for the egg wash. Leave the third bowl empty for the coated fish fillets.
Dip each fish fillet into the flour, coating it thoroughly and shaking off any excess flour. Then dip it into the egg wash, ensuring it is evenly coated.
Pour olive oil into your largest non-stick frying pan, ensuring it is about 1-2 inches in depth. Heat the pan over medium-high heat, allowing the oil to reach a temperature suitable for frying.
Once the oil is hot, gently place the coated fish fillets into the pan. Ensure they are not overcrowded; you may need to fry them in batches. Cook the fillets for approximately 2-3 minutes on each side or until they are golden brown and crispy.
Use a slotted spatula to remove the cooked fish fillets from the pan and place them on a plate lined with paper towels to absorb any excess oil. If desired, garnish with a squeeze of fresh lime or lemon juice before serving.