Beat the cream cheese in a large bowl with an electric mixer until soft. Add the cream, sugar, lemon zest and vanilla and beat until it just holds stiff peaks.
Spread the bottom of a 9-by-13-inch baking dish with 1/2 cup of the whipped cream. Arrange half of the cookies on top of the cream, fitting in as many as possible without overlapping. Spoon half of the remaining cream mixture on top and smooth evenly with an offset spatula. In spoonfuls spaced every 2 inches, dollop half of the lemon curd onto the cream and then use a butter knife to swirl the curd into the cream. Top with another layer of cookies, followed by the remaining cream. Dollop with the remaining lemon curd and swirl into the cream. Cover with plastic wrap and refrigerate until the cookies have softened, at least 3 hours and up to 1 day.
Garnish each serving with lemon zest when ready to eat.