Unroll the crescent rolls and press into a 10x15-inch pan (or place on a parchment paper-lined cookie sheet), making sure to seal any seams. Bake until puffed and golden brown, 11 to 13 minutes. Place the pan on a wire rack to cool completely.
Using an electric mixer, beat the cream cheese at medium speed until soft and smooth, about 2 minutes. Gradually add the sugar and beat until completely combined, then mix in the vanilla extract. Using an offset spatula, spread the cream cheese mixture over the cooled crust.
Top with assorted fruit of your choice. Serve immediately, or cover and refrigerate for up to 2 days.
Mini Versions: You can cut rounds out of the crescent dough to make little individual pizzas (kids would love to help make their own!).
Shape: If you have a round pizza pan, you can press your "crust" into that for a more traditional pizza shape!
Optional Glaze: To create extra shine on the fruit, you can brush it with apricot jam or honey that has been thinned a little with water.
Make-Ahead: You can prepare the crust and top it with the cream cheese frosting the day before serving, but don't add the fruit until the day you plan to serve it, within a few hours is best. The fruit will begin to break down and will make the filling runny and the crust soggy.
Transporting: If you make this to take to a picnic or BBQ, wait until the last possible moment to add the fruit to the top, cover tightly with plastic wrap, and keep it as cool as possible for the trip.
Storage: Cover leftovers with plastic wrap and keep in the refrigerator for up to 2 days. Expect that it will begin to get a bit soggy after the first day.