Preheat your oven to 350°F (175°C). Line a 12-inch round pizza pan or large rimmed baking sheet with parchment paper, or spray generously with non-stick cooking spray. Set butter and cream cheese out to soften at room temperature.
In a medium bowl, whisk together the flour, baking powder, and salt until combined. Set aside.
Using a stand mixer or hand mixer, beat the softened butter and granulated sugar on medium speed for 2 to 3 minutes until pale and fluffy. Add the egg, vanilla extract, and almond extract (if using) and beat until smooth. Add the flour mixture and mix on low just until no dry streaks remain; do not over-mix.
Transfer the dough to the prepared pan and press it out evenly into a 12-inch circle about 1/4 inch thick, working from the center outward. Dock the surface by poking several holes all over with a fork to prevent bubbling.
Bake for 12 to 14 minutes until the edges are lightly golden and the center still looks slightly underdone. Transfer the pan to a wire cooling rack and allow the crust to cool completely, at least 30 minutes, before adding any frosting.
Beat the softened cream cheese and butter together on medium-high speed for 2 minutes until smooth. Add the sifted powdered sugar and vanilla extract, beat on low until incorporated, then increase to medium-high and beat for 1 to 2 minutes until fluffy. Refrigerate until the crust is fully cooled.
Wash all fruit and pat completely dry with paper towels. Hull and slice the strawberries, peel and slice the kiwi, drain the mandarin segments and press dry, and halve the grapes lengthwise. Leave blueberries and raspberries whole.
Spread the chilled cream cheese frosting in an even layer over the completely cooled crust, leaving a 1/2-inch border around the edge. Work gently with a rubber spatula so the cookie doesn't break.
Arrange the prepared fruit over the frosting in concentric circles, rows, or a free-form pattern, alternating colors for maximum visual impact. Press each piece lightly into the frosting so it adheres.
Melt the apricot jam or apple jelly with 1 tablespoon of warm water in a small saucepan over low heat, stirring until smooth, about 1 to 2 minutes. Let cool slightly, then brush a thin, even layer over all the fruit with a pastry brush.
Refrigerate the assembled fruit pizza for at least 20 to 30 minutes to allow the frosting to firm up. Slice into 10 to 12 wedges with a sharp knife or pizza cutter and serve immediately.