Preheat the oven to 350°F (175°C).
In a large mixing bowl, combine the creamy peanut butter, granulated sugar, and light brown sugar. Mix until smooth and creamy.
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, mixing until just combined to form the cookie dough.
Press the dough evenly into a 12-inch round pizza pan or baking sheet lined with parchment paper, forming a flat crust.
Bake the crust in the preheated oven for 12 to 15 minutes, or until the edges are lightly golden.
Remove the crust from the oven and allow it to cool completely on a wire rack.
While the crust is cooling, prepare the frosting by beating together the softened cream cheese and unsalted butter until smooth and creamy.
Add the powdered sugar, 1 teaspoon vanilla extract, and plain Greek yogurt to the cream cheese mixture. Beat until smooth and fluffy.
Once the cookie crust is completely cooled, spread the cream cheese frosting evenly over the crust.
Arrange the sliced strawberries, blueberries, kiwi slices, and mandarin orange segments evenly over the frosting to create a colorful fruit topping.
Refrigerate the peanut butter cookie fruit pizza for at least 30 minutes before slicing and serving to allow the frosting to set.