Step 1

In a medium bowl, whisk the egg yolks with the milk. Spread the flour and bread crumbs in 2 separate wide, shallow bowls; season with salt.

Step 2

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.

Step 3

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 crispy outside 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 oil and fish.

Step 4

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.