Place lemon juice in saucepan over medium heat; simmer until lemon juice reduces to less than a tablespoon and almost disappears, 4 or 5 minutes, being careful not to let it burn. Quickly add cream; whisk to combine. Continue to cook until cream reduces and is thick enough to coat the back of a spoon, 5 or 6 minutes. Reduce heat to low.

Whisk in 2 or 3 pieces of cold butter, stirring until butter melts before adding more. Add 2 or 3 more butter cubes. (If cream mixture cools too quickly, the sauce may break.) Continue adding butter a few pieces at a time until all butter is emulsified into the cream, 8 to 10 minutes. Add salt, cayenne pepper, and 2 generous tablespoons chopped parsley. Whisk until well blended. Keep sauce warm until ready to use.