Preheat the oven to 325 degrees F (165 degrees C).

Combine graham cracker crumbs and sugar in a bowl; add melted butter. Mix until evenly moistened; press into the bottom and sides of a 9-inch pie plate. Bake in the preheated oven until crust begins to brown, about 10 minutes. Cool on a wire rack for 15 minutes.

Whisk sweetened condensed milk, lime juice, and sour cream together in a large bowl until combined; stir in lime zest. Pour filling into crust. Bake until tiny bubbles begin to form on surface of pie, 7 to 10 minutes. Cool completely on a wire rack.

Beat heavy cream, confectioners' sugar, and vanilla extract in a chilled glass or metal bowl with an electric mixer on medium speed until stiff. Top pie with whipped cream. Chill at least 1 hour before serving. Best served the same day.