In a medium pot, add the berries and cook until softened about 15-20 minutes.
Use a blender or immersion blender and blend the berries until smooth. Strain through a sieve to get all of the seeds out.
Put the mixture back in the pot and heat over low-medium heat. Add the honey and lemon juice and stir.
Stir together the cornstarch and water and add it to the berries. Allow the mixture to simmer until thickened.
Allow the mixture to cool. It is best to place this in the fridge to cool and thicken.
For the dough, place the flour, sugar, salt, and butter in a blender or food processor and pulse until the butter resembles small crumbs.
Slowly pour the water in just until the mixture comes together in a ball.
Divide the dough in half. Shape into discs, wrap in plastic wrap, and place in the fridge to chill until hardened, about an hour.
On a lightly floured surface, roll one of the discs out into about an 8 x 14 inch rectangle. Trim off any uneven edges. Cut the dough in half lengthwise, then cut 3-4 squares that are about 3-4 inches wide.
Place 1-2 tablespoons of the berry filling on half of them. Get a small bowl of water and dip your finger in it and rub it along the edges of the dough with the filling, then place the other piece of dough on top. You should have 3-4 pop-tarts.
Repeat with the remaining dough until you have 10-11 pop-tarts.
Use a fork to crimp the edges, then use a knife to cut a small slit in the tops of the pop-tarts.
Place them on a baking sheet lined with parchment paper and place in the fridge to chill for 20 minutes.
Preheat the oven to 375 degrees F.
Brush the pop-tarts with the egg wash and bake for 20-25 minutes, until golden brown.
Allow to cool.
While cooling, place 1 cup of powdered sugar in a bowl and add 1 teaspoon of water at a time until you get a thick enough consistency to spread, but not too runny. Add desired amount of purple food coloring to this bowl.
In a small bowl, add ½ cup powdered sugar and water until you reach a good consistency. Add desired amount of blue food coloring.
Spread the purple icing on the cooled pop-tarts and allow to sit until hardened, about 5 minutes.
Place the blue food coloring in a plastic bag, cut one of the corners off, and drizzle the blue icing over top of the purple icing.