Combine the flour, cornstarch, Confectioner’s sugar, salt, baking soda, and baking powder in the bowl of a food processor. Pulse to blend.

Add the butter, and pulse 4 to 5 times until it forms a sandy-looking mixture with some pebble-size pieces.

Pour in the cream. Pulse a few times, then process 30 to 60 seconds until it comes together in a rough ball.

Place the dough on a lightly floured counter or cutting board. Gently knead a few times until it comes together into a smooth dough.

At this point, you can wrap the dough, chill it up to 2 days, until ready to use (let it soften enough to roll if you choose to do so), or continue making these Peach Pop Tarts.