The glory of a galette is in its imperfection, so don’t stress about rolling the (store-bought!) dough into a perfect circle. Aim for rustic, and you’ll end up with gorgeous.
Preheat oven to 425 degrees F. Line a baking sheet with parchment paper. Roll piecrust into a 12-inch circle on a lightly floured work surface; place on prepared baking sheet.
Toss together blackberries, blueberries, flour, lemon juice, and 1/3 cup of the sugar in a bowl. Arrange mixture evenly over dough, leaving a 3-inch border. Fold dough edges up and in toward center, pressing gently among folds to seal. (Dough will only partially cover berry mixture.) Brush melted preserves over exposed berry mixture. Brush beaten egg over piecrust. Sprinkle piecrust with remaining 1/2 tablespoon sugar.
Bake for 10 minutes. Reduce oven temperature to 350 degrees F (leaving galette in oven); bake until galette is golden brown and filling is bubbly, 15 to 20 minutes more. Transfer to a wire rack; let cool 1 to 2 hours. If desired, serve with ice cream or frozen yogurt.