Whisk the egg yolks with the milk in a medium bowl. Spread the flour and breadcrumbs in 2 separate wide, shallow bowls; season both with salt.
Dredge the fish in the flour, dusting off the excess. Dip the fish in the egg mixture, then dredge it in the breadcrumbs. Transfer the fish to a large plate.
Melt 2 tablespoons of the butter in 2 tablespoons of the olive oil in a 12-inch cast-iron skillet. 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.
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.
