Filling and assembly
Preheat oven to 350. Toast pecans on a rimmed baking sheet, tossing once, until fragrant and slightly darkened, 10-15 min, let cool. Pulse pecans in a food processor until the consistency of coarse meal. Add flour, sugar, salt, and cinnamon and pulse to combine. Add butter and pulse until mixture resembles coarse meal with a few pea size pieces remaining.
Transfer to a large bowl; drizzle with 4 TBL ice water and mix just until mixture comes together. Gently pat dough into a 6" diameter disk. wrap in plastic and chill at least 1 hour.
Filling and Assembly
Preheat oven to 375. Toss persimmon filling together in a large bowl.
Roll out dough on a lightly floured surface to a 13" round. Carefully transfer to a parchment lined baking sheet. Arrange persimmon slices in center of dough, leaving a 2" border. Fold edges over, overlapping slightly. Brush dough with milk and sprinkle with sugar.
Bake galette until crust is dark golden brown and filling is bubbling, 45-50 min. Let cool before serving.