Put flour, salt, and sugar in bowl of a food processor, and pulse to combine.
Add butter, and process for about 10 seconds, or just until the mixture resembles coarse meal.
Add ice water, tablespoon by tablespoon (1/4 to 1/2 cup), through the feed tube with machine running, just until the dough holds together without being wet or sticky; do not process more than 30 seconds.
Test the dough at this point by squeezing a small amount together. If it is crumbly, add a bit more water.
Wrap the dough in plastic wrap, using a rolling pin to flatten into a disk.
Chill until needed.
Make the galette rounds
Divide dough evenly into 8 pieces.
On a lightly floured surface, roll out each piece to a 7-inch round, 1/8 inch thick.
Transfer rounds to 2 large parchment lined rimmed baking sheets, arranging several inches apart. (If rounds become too soft to handle, refrigerate until firm, about 20 minutes.)
Make the filling
In a large bowl, toss to combine berries, cornstarch, and granulated sugar.
Cover each round of dough with a heaping ½ cup berry mixture, leaving a 1-inch border.
Fold edges over filling, in a pleated, accordion style, leaving an opening in center.
Gently brush water between folds, and press gently so that folds adhere.
Zest lemon over each galette.
Refrigerate or freeze until firm, about 30 minutes.
Bake the galettes
Preheat oven to 400º F.
In a small bowl, mix egg with water. Brush edges of dough with egg and water mixture, and sprinkle with coarse sugar.
Bake until crusts are golden brown, about 30 minutes. Reduce heat to 375º F, and bake until juices bubble and start to run out from center of each galette, about 15 minutes more.
Transfer to a wire rack, and let cool completely before serving.