Crust: Pulse flour, sugar, and salt in a food processor to combine. Add butter; pulse until mixture resembles coarse crumbs. Add yolks and ice water; pulse until dough comes together. Pat into a disk, wrap in plastic, and refrigerate at least 1 hour or overnight.
Let dough stand at room temperature until pliable. Roll out on a lightly floured surface to a rough 13-inch round, about 1/4 inch thick. Fit into an 11-inch fluted tart pan with a removable bottom. Fold over and tuck overhanging edges into pan. Freeze until firm, about 1 hour.
Filling: Toss to combine plums, both sugars, cornstarch, salt, and rose water in a bowl. Spread in tart shell in a single layer.
Crumble: Combine brown sugar, butter, flour, and salt in a bowl and mix with fingertips until clumps form. Crumble evenly over filling.
Preheat oven to 400 degrees with rack in lower third. Bake on a rimmed baking sheet until juices are bubbling and topping is browned, about 50 minutes. Let cool completely. Tart is best served the day it's made, with sorbet.