In the stand mixer with a paddle attachment (or use a large bowl and a beater), beat the cream cheese on high for 1 minute to soften. Add the confectioners’ sugar, and continue beating on low speed until combined. Stop to scrape down the sides of the bowl, then beat on high until light and fluffy, about 2 minutes. (If using a stand mixer, switch to the whisk attachment). With the mixer on low, slowly add the cream, a tablespoon or two at a time, beating after each addition until the mixture is smooth. Scrape down the sides of the bowl, add the vanilla and increase speed to high and beat until billowy and whipped, about 2 more minutes. Transfer to the cooled crust and spread in an even layer. Cover with plastic wrap and refrigerate until chilled, at least 2 hours, before topping.