Combine flour and salt in a bowl. Add cold, cubed butter and work into the flour with your hands. Gradually add ice water, 1 tablespoon at a time, until the dough comes together. Chill dough for at least one hour.
While dough is chilling, prepare filling. Mix all ingredients except lavender and beaten egg in a bowl. Preheat oven to 375°F.
When dough has chilled, roll out and cut into 24 (3- by 4-inch) rectangles. To assemble, spoon filling onto half of the rectangles, leaving a little room around all edges. Sprinkle lavender over the berries and brush egg wash around edges of dough. Place remaining rectangles over filling and crease all edges with a fork. Brush remaining egg wash on top of pop tarts and place on a baking sheet covered with parchment paper. Bake for 30 minutes. Immediately place pop tarts on a cooling rack.
While pop tarts are cooling, make glaze. Sift powdered sugar in a medium bowl and whisk in milk until it is pouring consistency. When pop tarts are completely cooled, cover each with glaze.