Using a stand mixer or a hand mixer, beat together the cream cheese and butter until smooth.
Add the vanilla and beat until combined. Slowly add the sugar and beat until smooth. Add the cream or milk a little at a time until desired consistency.
Notes
Assembly
Divide the cake into two even layers using a serrated knife or cake leveler (like this).
Wrap each layer with plastic wrap and freeze for at least 4 hours (overnight preferred).
Place one layer on a serving platter or cake stand. Pipe a ½-inch border of cream cheese frosting along the edge of the cake. Using a small offset spatula, spread about ½ cup of lemon curd within the boundaries of the cream cheese border.
Cover with the second frozen layer, top-side down.
Using an offset spatula, cover the entire cake evenly with the remaining cream cheese frosting.
Decorate with zest if desired. Cut into 9 even squares.
Storage Store at room temperature for up to 4 days.