For the Crumb Topping: Whisk the granulated sugar, dark brown sugar, cinnamon, ginger, and salt into the melted butter in a medium bowl to combine. Add the flour and stir with rubber spatula or wooden spoon until the mixture resembles thick, cohesive dough; set aside to cool to room temperature, at least 10 to 15 minutes.
For the Rhubarb: Toss the rhubarb with the sugar, cornstarch, and ginger in a small bowl until evenly coated; set aside.
For the Cake: Adjust oven rack to upper-middle position and heat oven to 325 degrees F. Spray an 8-inch square baking dish with nonstick cooking spray and line with parchment paper, pushing it into corners and up sides; allow excess to overhang edges of dish.
With an electric mixer on low speed, mix the flour, sugar, baking soda, and salt on low speed to combine. With the mixer running at low speed, add butter one piece at a time; continue beating until the mixture resembles moist crumbs, with no visible butter chunks remaining, 1 to 2 minutes. Add egg, yolk, vanilla, and buttermilk; beat on medium-high speed until light and fluffy, about 1 minute, scraping the bowl once if necessary.
Use a slotted spoon to remove the rhubarb from the bowl where it will have released some juice. Add the drained rhubarb to a clean bowl. Toss the rhubarb with the 2 teaspoons of all-purpose flour, coating it evenly. Add the rhubarb to the cake batter and gently fold it into the batter using a rubber spatula.
Transfer the batter to the prepared baking pan; using a rubber spatula, spread the batter into an even layer. Break apart the crumb topping into large pea-sized pieces and spread in even layer over batter, beginning with the edges and then working toward center. Bake until crumbs are golden and wooden skewer inserted into center of cake comes out clean, 55 to 65 minutes. Cool on a wire rack at least 30 minutes. Remove cake from pan by lifting parchment overhang. Dust with powdered sugar just before serving.