Mixed Berry Breakfast Pastries

Name: Mixed Berry Breakfast Pastries
Prep time: 2 h
Cook time: 55 min
Total time: 2 h 55 min
Cuisine: American
Ingredients: 250 grams fresh or frozen mixed berries (2 cups; 9 ounces); 150 grams granulated sugar (3/4 cup); Juice of 1/2 lemon; 2 sheets puff pastry, thawed according to package directions if frozen; 1 egg, lightly beaten; 100 grams confectioner’s sugar (3/4 cup); 15 milliliters whole milk (1 tablespoon); 1 teaspoon vanilla bean paste or vanilla extract; Purple gel food coloring (I used Neon Brite Purple)