In a large mixing bowl, combine the flour, Parmesan, black pepper, and sea salt. Grate in the butter, then mix it into flour with your fingertips.
In a small bowl, combine sour cream and ice water. Drizzle over flour mixture, using a Silicone spatula to fold in the liquid. Turn out onto a lightly floured surface, gather into a disc, and wrap tightly with plastic. Chill in refrigerator for 30 minutes (or an hour or more if it's a hot, humid day).
Preheat oven to 425° F. Set out a rimmed baking sheet.
Core and cut tomatoes into 1/4-inch slices. Use your fingertips to scoop out all the seeds you can, then line a plate with paper towels, scatter the tomato slices over top, and sprinkle with sea salt. Cut plums into 1/4-inch slices.
On a lightly floured sheet of parchment, roll dough into a rough 14-inch circle. Brush any excess dough or flour from the parchment, reserving leftover dough. Scatter 2 tablespoons Parmesan in a 12-inch circle in the center of the dough circle. Next, arrange a band of tomatoes around this 12-inch circle. Working inwards, alternate circles of plums and tomatoes, tucking each layer against the other so they stand up at a diagonal. Working quickly, fold up the sides of galette, pressing along each seam. If needed, use any excess dough to patch holes. Lightly brush edges with the egg and sprinkle with a generous pinch each sea salt and pepper.
Carefully lift parchment, galette and all, onto a rimmed baking sheet. Trim parchment as needed. Bake at 425° F for 10 minutes. Pull galette out of oven, sprinkle with remaining Parmesan, rotate pan, and slide back into oven. Lower heat to 375° F and bake until galette is a rich golden brown, 20 to 25 minutes more.
Cool for 15 to 20 minutes, scatter tarragon leaves over the top, and then serve warm.