Tossing constantly with a fork, drizzle in ⅓ cup plus 1 Tbsp. ice water, then using your hands, lightly toss the mixture several times to distribute water evenly. Knead dough in the bowl with your hands until it comes together into a smooth mass with no spots of dry flour remaining. Transfer dough to a sheet of wax paper or plastic wrap and pat into a ½”-thick square. Wrap tightly, pressing out air, then roll over dough with a rolling pin in both directions, forcing it into the corners of the wrapping to make a tightly compacted square. Chill at least 2 hours and up to 36 hours ahead.
Filling
Preheat oven to 250°. Combine strawberries, granulated sugar, salt, and 3 Tbsp. water in a large saucepan and cover. Bring to a simmer over medium heat, uncovering and stirring occasionally, until berries are softened, about 5–8 minutes. Remove from heat and purée with a hand blender, leaving a bit of texture if you like (or, transfer to a standard blender and blend, then return to the saucepan). Return to a simmer, uncovered, and cook, stirring often with a heatproof rubber spatula, being sure to scrape the sides and bottom of pan, until filling is thick enough that you can see the bottom of the pot for a second when you scrape the spatula across, 10— 15 minutes.
Scrape filling onto a large rimmed baking sheet lined with a silicone mat and spread into a thin, even layer. Bake, stirring every 15 minutes with spatula, until it becomes a thick paste that holds its shape (it should resembles tomato paste), 45–60 minutes. Let cool, then transfer filling to a small bowl and stir in vanilla. Add lemon zest and juice to taste.
Do ahead: Filling can be made 1 week ahead. Cover and chill.
Sprinkles
Whisk egg white and a pinch of kosher salt in a medium bowl until foamy. Add powdered sugar a little bit at a time, whisking constantly and vigorously until you have a thick, smooth, opaque white icing (depending on the size of your egg white, you might not need all the sugar). Divide icing among 5 small bowls and, working one at a time, add food coloring a drop at a time, stirring with a spoon, until you have the desired color. Repeat until you have all 5 sprinkle colors: orange, red, pink, green, and yellow. Spread each color icing in an even strip across a sheet of parchment paper, making as thin a layer as possible. Slide parchment paper onto a baking sheet and let sit at room temperature until icing has dried and hardened completely, at least 12 hours.
Peel icing off of parchment paper and break into smaller pieces with your hands. Place the pieces inside a resealable plastic bag and seal, pressing out any air. Beat the bag lightly with a rolling pin to pulverize the icing into tiny sprinkles. Transfer the sprinkles to a fine mesh sieve and shake to remove any tiny, dust-like particles; discard. Pass sprinkles through a colander or slotted spoon, reserving the pieces that fall through and returning any larger pieces that don’t to the bag and breaking up further with rolling pin. Repeat the double-sifting process until you have very small, relatively uniform sprinkles. Transfer to an airtight container, cover, and store at room temperature until you’re ready to assemble pop tarts.
Do Ahead: Sprinkles can be made 1 week ahead.
Assembly
Preheat oven to 300°. Unwrap dough and cut in half. Re-wrap one half and return to the refrigerator. Roll out remaining dough on a lightly floured surface to about 14x10” rectangle. Transfer to a baking sheet lined with parchment paper.
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