How to Make It
In a medium bowl, whisk the egg yolks with the milk. Spread the flour and bread crumbs in 2 separate shallow bowls and season with salt.
Dredge the fish in the flour, dusting off the excess. Dip the fish in the egg mixture, then dredge in the bread crumbs. Transfer to a large plate.
In a 12-inch cast-iron skillet, melt 2 tablespoons of the butter in 2 tablespoons of the olive oil. Add 2 fish fillets and cook over moderate heat, turning once, until golden and white throughout, about 6 minutes. Transfer the fish to plates. Wipe out the skillet and repeat with another 2 tablespoons of butter and the remaining 2 tablespoons of oil and fish.
Wipe out the skillet. Whisk in the remaining 4 tablespoons of butter and the 2 tablespoons of lemon juice; season with salt. Spoon the sauce over the fish, garnish with parsley and serve with lemon wedges.