Add the flour, powdered sugar, and salt to the bowl of a food processor. Pulse until combined. Add in the butter and pulse 7 times. With the processor running, pour in the milk and process until the dough forms a cohesive ball.

Scrape the dough from the bowl and place it onto a piece of plastic wrap. Form the dough into a rectangle and wrap tightly. Using a rolling pin, roll the dough out until it stretches to the edges of the plastic wrap to ensure a tight seal.

Refrigerate for at least 2 hours, but preferably overnight.

In a medium pot, combine the mixed berries, sugar, and salt. Cook over medium heat until bubbling. Reduce the heat to medium-low and simmer for 5 minutes.

Shut off the heat.

Transfer the berries into a medium bowl. Set the pot back on the stove as is.

Using an immersion blender (or a regular blender), puree the berry mixture.

To the pot, stir together the lime juice and cornstarch. Set a fine-mesh strainer. Strain the berry mixture into the pot and stir together to combine with the lime-cornstarch slurry.

Return the heat to medium and bring the filling to a boil. Once the mixture has thickened, remove it from the heat.

Chill the filling for at least 12 hours, or overnight.

Remove the chilled dough from the refrigerator and let it rest at room temperature for 5 to 10 minutes, or until it is slightly softened and easier to roll. Then, divide the dough in half.

On a well-floured work surface, roll out one piece of dough to a rough 9-by-13 rectangle, about ⅛-inch thick. Using a pastry wheel or chef’s knife, cut out as many 3-by-4-inch rectangles as you can. Repeat with the remaining dough. Then, gather up the scraps and roll out the dough in the same manner, cutting out as many rectangles as possible. This dough should yield 16 to 18 rectangles total. If the dough is very warm once all rectangles are cut, briefly chill them down in the refrigerator for 15 minutes.

Line a baking sheet with parchment paper and place half of the rectangles down on the baking tray.

Use a pastry brush to brush the egg wash around the edges of the pastry.

Place 1 heaping tablespoon of the berry filling in the middle of each rectangle. Place the remaining pastry rectangles on top, taking care to seal the edges well. Use a fork to crimp the edges. Finally, using a bench scraper, trim the edges of the pastry. This makes the final product look neat and also seals the pop tarts well.

Chill the tray of pop tarts in the refrigerator for at least 30 minutes.

Preheat the oven to 375°F and place an oven rack in the middle part of the oven. Bake the pop tarts in the preheated oven until the bottoms are slightly golden, about 25 minutes. Transfer to a wire rack and let cool completely.

In a small bowl, whisk together the powdered sugar, 2 tablespoons of the berry puree, and vanilla. The glaze should be thick enough to keep its shape for a few seconds when drizzled off of a spoon; if it’s too thick, add in more berry puree or water as needed.

Spoon 1 tablespoon of glaze onto the middle of each cooled pop tart and gently smooth it down. Add sprinkles or coarse sugar before the glaze sets.