Preheat oven to 375 degrees. In a processor, mix all dry ingredients and pulse a few times. Add butter and process until butter is about pea-sized, approx. 1 min. Drizzle in water while processor is running and mix until dough comes together (will be slightly wet). Shape dough into a rough disc, cover tightly with plastic wrap and chill at least 1 hour (can be made 2-3 days in advance). When dough is chilled, lightly flour a work surface, using enough flour to easily lift dough. Roll dough out to a 12" rough circle. Line sheet pan with parchment paper. Transfer dough to sheet pan and add cherry filling to center, leaving 2" borders. Fold up sides, overlapping/pleating every few inches. Egg wash each pleat to keep its shape while baking. Brush all exposed dough (sides and top) with egg wash and sprinkle generously with turbinado sugar. Chill tart for 15 min before baking. Bake 40-45 min, rotating at 30 min, until crust is a deep golden color and cherries have begun to release juices. Let tart cool 10-15 min before cutting. Serve with vanilla ice cream or whipped cream, as desired.
Combine pitted and halved cherries with remaining ingredients. Let rest 20 min at room temperature. Fill tart as described above.