To make pie crust: Add the flour, sugar, and salt to the bowl of a food processor. Pulse to combine. Add the butter and pulse until the mixture resembles coarse crumbs with some larger pieces remaining, about 10 seconds. With the processor running, slowly pour in about half the water in a slow steady stream: stop when the dough holds together without turning wet or sticky. Do not process more than 30 seconds. Test by squeezing a small amount of dough together; if it is still too crumbly, then add a bit more water, one tablespoon at a time.
Divide the dough into 2 balls and flatten each into a flat rectangle shape. Wrap each in plastic wrap and place in the fridge for at least an hour.
To make the filling: Combine the mixed berry jam and agar-agar in a saucepan and heat on high until it begins to boil. Pour into a bowl and place in the fridge to cool.
When the pie dough is ready, roll out the first piece on a floured surface until it is about a couple inches wider and longer than your sheet pan on either side. Gently place the dough onto the pan, pressing it firmly into the corners. Fill the pan with your filling, smoothing it out. Roll out the second piece of dough the same as the first. Place it over the top of the pan. Using a fork, crimp around all of the edges of the pan. Cut off any excess dough hanging over the sides of the pan and cut some small vent holes across the top crust layer.
Bake at 400°F for about 45 minutes, until the top is lightly golden brown. Allow to cool slightly on a wire rack.
To make frosting: Combine the powdered sugar, milk, and corn syrup into a bowl, stirring until achieving a thick frosting-like consistency. Separate out 2 Tbsp of the frosting into a smaller bowl. Use food coloring to make the large bowl of frosting purple and the small bowl blue.
To assemble: Spread the purple frosting over the warm Pop-Tart. Using a piping bag with a small tip, zig zag the blue frosting across the top of the Pop-Tart. Enjoy!