In a mixing bowl, combine the all-purpose flour, sugar, and salt. Whisk until well mixed.
Add chilled, cubed butter into the bowl. Using a pastry cutter or your fingers, blend until the mixture resembles coarse crumbs.
Mix in the active sourdough starter, milk, and vanilla extract until a dough forms.
Turn the dough out onto a lightly floured surface and gently knead it a few times until smooth. Wrap in plastic wrap and refrigerate for at least 30 minutes.
Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
Once chilled, roll out the dough on a floured surface to about ⅛ inch thick. Cut into rectangles (approximately 3x4 inches) to create 16 pieces.
On half of the rectangles, place about 1 tablespoon of fruit preserves or jam in the center.
Moisten the edges of the dough with water, then place the second rectangle on top and press the edges to seal. Use a fork to crimp the edges for a decorative effect and to ensure they are sealed tightly.
Transfer the pop tarts to the prepared baking sheet and brush the tops with egg wash.
Bake for 20-25 minutes or until golden brown. Remove from the oven and allow to cool on a wire rack.
If desired, dust with powdered sugar before serving.