Rinse the fillets, pat dry with a paper towel.
In a shallow dish, mix together the flour, salt, and pepper.
Coat each fillet in the flour mixture. Shake off any excess.
In a large nonstick skillet, heat the butter and olive oil over medium-high heat until the butter melts and the mixture is sizzling.
Add the fillets to the skillet. Cook for 2 to 3 minutes on each side until golden brown and cooked through.
Remove the fillets from the skillet and transfer to a plate lined with paper towels to absorb excess oil.
Serve the sole with lemon wedges and chopped parsley, if desired.
