Make crust: Combine dry ingredients in a stand mixer. Add butter and beat with paddle attachment on low speed, scraping bowl as needed, until pieces are raisin-size. With mixer still on low speed, drizzle in 1 tbsp. ice water; beat until pastry comes together, 1 1/2 to 3 minutes. Form 1 1/4 cups into a disk and the rest into a smaller disk.
Preheat oven to 375° with rack on bottom rung. On a lightly floured board, roll larger disk into a 12-in. circle. Loosen with a long metal spatula, gently roll around a rolling pin, then unroll into a 9-in. pie pan (if dough cracks, press back together). Fold edge under, so it's flush with pan rim, then crimp. Chill 15 minutes.
Roll remaining dough into an 11-in. circle. With a cookie cutter, cut out as many shapes, such as squares, as needed to cover most of pie. Set cutouts on a baking sheet; chill 15 minutes.
Make filling: Stir together cornstarch and granulated sugar in a large bowl. Add berries with juices and toss to coat. Arrange evenly in pie shell. Lightly brush pastry cutouts with water and sprinkle with coarse sugar. Arrange cutouts over filling.
Bake pie until filling bubbles and pastry is golden in center, 55 to 60 minutes (up to 1 1/2 hours if berries were frozen); if edge starts to get dark, cover with foil, and if pie starts to bubble over, put a rimmed pan underneath it.
Let cool on a rack to room temperature, at least 3 hours.
*Find sparkling sugar with the baking supplies.
Note: Nutritional analysis is per serving.