In a mixing bowl, combine the active sourdough starter, flour, sugar, and salt. Add the chilled butter cubes and mix until the mixture resembles coarse crumbs.

Add the milk and mix until a dough forms. Avoid overmixing; it should be soft and slightly sticky.

Wrap the dough in plastic wrap and refrigerate for at least 30 minutes.

After chilling, divide the dough into two halves. On a lightly floured surface, roll out each half to about ¼ inch thickness.

Using a pastry cutter or knife, cut the dough into rectangles (about 3x4 inches) for the pop tarts.

Place half of the rectangles on a lined baking sheet. Spoon about a tablespoon of jam or fruit preserves onto the center of each rectangle.

Place the remaining rectangles over the filled ones and press the edges together to seal. Brush the tops with a whisked egg.

Preheat your oven to 375°F (190°C) and bake for 20-25 minutes, or until golden brown.

Allow the pop tarts to cool slightly before glazing.

Mix powdered sugar with a little water or milk until it reaches your desired consistency. Drizzle over cooled tarts.