In a large deep saucepan, melt the butter and bring it to a mild simmer over moderate heat. Set the shad roe in the butter, cover, and poach gently for 10 to 12 minutes turning once. Meanwhile, prepare the sauce: Melt the butter in the saucepan set over moderate heat. When the foam subsides, remove the pan from the heat and whisk in the flour. Return the sauce to the heat, gradually pour in the half-and-half and whisk vigorously. Cook, whisking, until the sauce thickens about 10 minutes.

Season to taste with salt and pepper and fold in the sorrel.

When the shad roe are cooked, slide a slotted spoon under them, and remove to a heated serving plate.Set aside and keep warm.

Continue cooking the sauce for 2 to 3 minutes, stirring with a wooden spoon, until the sorrel wilts. Spoon the sauce over the shad roe.

Serve with steamed or boiled new potatoes, sprinkled with a combination of finely chopped lemon zest and cilantro.