Combine flour, 1 ½ teaspoons salt, and pepper in shallow bowl and whisk together.

Pat sole filets dry with paper flowers and dredge in flour mixture, shaking off excess

Melt butter in a large skillet over medium heat. Add filets to the hot butter and cook for 1 minute. Add lemon juice and lemon zest and cook until well browned on first side, 2 to 3 more minutes. Carefully turn fillets using 2 spatulas and cook until fish flakes easily with a fork, 1 to 2 minutes longer, tossing lemon butter mixture over the fish as it cooks.

Remove fish from pan and stir parsley into butter sauce. Season with remaining salt to taste. Stir and whisk together, then ladle butter sauce over fish fillets. Serve immediately with lemon wedges.