In a large bowl, whisk together the flour and 1/4 teaspoon of the salt. Add the cubes of chilled butter and work it into the flour mixture with a pastry cutter until it resembles a coarse meal with little pea-sized bits of butter. In a small bowl, stir together the sour cream, lemon juice, and water, and mix into the flour-butter mixture until large lumps form. Gently, without overworking the dough, pat into a ball. Cover with plastic wrap and refrigerate for 1 hour.
Spread the zucchini in an even layer over several sheets of paper towels. Sprinkle with 1/2 teaspoon of salt, and let drain for 30 minutes. Blot softly with paper towels. In a small bowl, combine the olive oil and garlic. In a separate bowl, fold together the ricotta, Parmesan, shredded mozzarella, and 1 teaspoon of the garlic olive oil. Season to taste with salt and pepper.
Preheat the oven to 400˚F. Lightly flour a work surface and roll out the dough into a 12-inch round. Transfer to a baking sheet. Spread the ricotta mixture in an even layer over the dough, leaving a 2-inch border. Layer the zucchini rounds over the ricotta, placing them in concentric circles, starting at the outside edge of the ricotta. Drizzle zucchini with the remining garlic olive oil. Gently fold the border of the dough over the outer edge of the filling. Brush the crust with the egg yolk and water mixture.
Bake 30-40 minutes, until the zucchini is wilted, the cheese looks puffy, and the crust is golden brown. Sprinkle galette with the basil and let sit for 5 minutes. Transfer to a serving dish and slice into wedges. Serve immediately, or at room temperature.