Preheat the oven to 350°F (175°C).
In a large bowl, combine the peanut butter, granulated sugar, and brown sugar. Mix until smooth.
Add the egg and 1 teaspoon vanilla extract to the peanut butter mixture and beat until well combined.
In a separate bowl, whisk together the baking soda, salt, and all-purpose flour.
Gradually add the dry ingredients to the peanut butter mixture, stirring until just combined.
Press the cookie dough evenly into a 12-inch round pizza pan or a rimmed baking sheet to form a flat crust.
Bake the crust for 12 to 15 minutes, or until the edges are lightly golden and the center is set.
Remove the crust from the oven and allow it to cool completely in the pan on a wire rack.
While the crust cools, prepare the frosting by beating the softened cream cheese and unsalted butter together in a medium bowl until smooth and creamy.
Add the powdered sugar and 1 teaspoon vanilla extract to the cream cheese mixture and beat until fully combined and smooth.
Spread the cream cheese frosting evenly over the cooled peanut butter cookie crust.
Arrange the sliced strawberries, blueberries, kiwi slices, mandarin orange segments, and halved grapes evenly over the frosting to create a colorful fruit topping.
Refrigerate the fruit pizza for at least 30 minutes before slicing and serving to allow the frosting to set.