Make the dough: Sift dry ingredients and transfer to a food processor. Add butter and cream cheese and pulse until pieces range from pea to hazelnut size. Add ice water to mixture. Pulse until dough just starts to come together. If it's too dry, add water 1 Tbsp. at a time. Pile dough onto a sheet of plastic wrap, wrap tightly into a disk, and chill for 1 hour or overnight.
Make the filling: Combine figs, 1 1/2 cups cranberries, wine, and brown sugar in a large saute pan over medium heat. Bring to a boil and reduce to a simmer until cranberries begin to pop, figs soften, and liquid thickens slightly, about 25 to 30 minutes. Transfer to a bowl and stir in remaining cranberries and red wine vinegar. Let cool completely. (You should have 1 1/2 cups filling.)
Roll dough on a lightly floured surface to 1/4 inch thick. Trim to a 10 1/2-inch circle. Transfer to a parchment-lined rimmed baking sheet. Brush a 1-inch border with egg wash. Pile filling toward center of dough and fold dough over about 2 inches. Pinch to seal. Brush with egg wash and sprinkle with granulated sugar. Chill until firm, about 30 minutes.
Preheat oven to 375 degrees. Bake tart until golden and bubbling, about 35 to 40 minutes. Let cool slightly before serving.