To make the dough by hand, stir the sour cream and 1/3 cup ice water together in a small bowl and set aside. Put the flour, cornmeal, and the butter pieces in another bowl. Toss once or twice just enough to coat the butter pieces with flour. With a pastry blender, work the butter into the flour, aiming for pieces of butter that range in size from breadcrumbs to small peas. The smaller pieces will make the dough tender, the larger ones will make it flaky.
Sprinkle the cold sour cream mixture over the dough, 1 tablespoon at a time, tossing with a fork to evenly distribute it. After you've added all the sour cream, the dough should be moist enough to stick together when pressed; if it's not, add additional cold water, 1 teaspoon at a time. With your hands, gather the curds of dough together. (You'll have a soft, malleable dough, the kind you might want to overwork.)
To make the dough in a food processor, stir the sour cream and 1/3 cup ice water together in a small bowl; set aside. Put the flour, cornmeal, sugar and salt in a processor fitted with a metal blade. Pulse to combine. Drop the butter pieces into the bowl and pulse 8 to 10 times, or until the mixture is specked with pieces of butter that vary in size from breadcrumbs to peas. With the machine running, add the sour cream mixture and process just until the dough forms soft, moist curds.
Turn the dough out of the bowl and divide it in half. Press each piece of dough into a disk, wrap in plastic, and refrigerate for at least 2 hours.
Each disk will make one galette large enough to serve 4 to 6.
Preheat the oven to 400 degrees. Line a baking sheet with parchment paper. On a lightly floured work surface roll out the dough into an 11-inch circle bout 1/8 inch thick. Since the dough is soft, you'll need to lift it now and then and toss some more flour under it and over the top. Roll up the dough around your rolling pin and transfer it to the prepared baking sheet.
Spread the berries over the dough, leaving a 2-to 3-inch border. Sprinkle 1 1/2 tablespoons of sugar over the berries. Cut the butter into slivers and scatter on top of the fruit. Fold the uncovered border of dough up over the filling, allowing the dough to pleat as you lift it up and work your way around the galette. (It won't be perfectly symmetrical, that's part of the charm of galettes.) Dip a pastry brush in water, give the edge of the crust a light coating, and then sprinkle the crust with the remaining sugar.
Bake for 35 to 40 minutes, or until the pastry is golden and crisp. Transfer the baking sheet to a cooling rack and let the galette rest on the sheet for 10 minutes. Slip a wide spatula or a small baking sheet under the galette and slide it onto the cooling rack. Serve warm or at room temperature.