In a food processor, pulse together the flour, sugar, salt, and butter until the butter resembles pea-sized pieces. Slowly stream in the cold water while pulsing until the dough comes together.
Transfer the dough to a floured surface, gently knead into a ball, and shape into a rectangle about 1/2-inch thick. Wrap in plastic and refrigerate for 2 hours.
Meanwhile, blend strawberries, honey, and lemon juice until smooth. Strain through a fine mesh sieve into a saucepan to remove seeds.
Cook over medium heat for 20–25 minutes, stirring occasionally, until thickened to a jam-like consistency. Let cool completely.
Preheat the oven to 300°F (150°C) and line a baking sheet with parchment paper.
Roll out half the dough into a 14 x 14-inch square, about 1/8-inch thick.
Cut into rectangles (approximately 3.5 x 4.75 inches). Repeat with remaining dough, re-rolling scraps as needed.
Spoon about 1 tablespoon of filling onto half of the rectangles, spreading evenly and leaving a border. Brush edges with beaten egg yolk.
Dock the top pieces with a fork, place over the filled bases, press edges together, and crimp to seal.
Bake for 30–35 minutes, until lightly golden.
Whisk powdered sugar and milk to form a thick glaze. Once pop tarts are cooled, spread glaze on top and add sprinkles if desired.