Combine the wine, lemon, shallots, and garlic in a medium saucepan and bring to a boil. Reduce the heat to medium-low and simmer until reduced by half, about 10 minutes, stirring occasionally and mashing the lemon pieces with the back of a spoon. Add the cream and cook until reduced by half, about 3 minutes.

Whisk in the butter, 1 tablespoon at a time, adding each piece before the previous one has been completely incorporated. Continue until all the butter is incorporated and the sauce coats the back of a spoon, removing the pan from the heat periodically to prevent the sauce from getting too hot and breaking. Add the salt and pepper, and whisk to blend.

Remove from the heat and strain, pressing down with the whisk, through a fine mesh strainer, into a small bowl. Fold in the parsley and cover to keep warm.