Steam the potatoes until tender.

Clean and gut the sole. Pat dry thoroughly with paper towels, then season with salt and pepper. Place the flour in a shallow dish and dredge the fish in it. Shake off any excess flour. This helps the fish hold together while cooking.

Wash the lemon and parsley. Slice the lemon into rounds and roughly chop the parsley.

Heat oil and 2 tablespoons (25 grams) of butter together in a skillet. Once the butter has melted, cook the sole for 5 minutes on each side over medium heat. While cooking, continuously baste the fish with the browned butter (the butter should be melted and lightly golden). Be careful not to burn the butter—keep it at a light brown color by adjusting the heat as needed. Once cooked, place the sole meunière on a warm serving dish, white skin side down.

Brown the potatoes in the skillet with some butter.

Garnish the sole with parsley and a squeeze of lemon juice.