1. Add milk to the fillets with milk barely to cover and let stand about 15 minutes. Pat the fillets dry and dredge in seasoned flour.
2. Add the peanut oil to a large skillet to a depth of 1/4 inch. When it is hot, cook the fillets on both sides until golden brown. Transfer the fillets with a spatula to a hot dish and pour off and discard the oil in the skillet.
3. Add the butter to the skillet and, when it starts to brown, pour it over the sole fillets. Sprinkle with lemon juice and chopped parsley and garnish with lemon slices dipped in parsley.