Make dough: Put flour, granulated sugar, and butter in a food processor and pulse until butter resembles coarse crumbs. Add egg yolk and pulse until combined. Add cream 1 tbsp. at a time and pulse until dough begins to come together. Transfer to a work surface and gently knead to bring together. Divide dough in half, shape each into a 1/2-in.-thick disk, and wrap in plastic wrap. Chill until firm, 30 to 60 minutes.
Meanwhile, make crostata filling: Toss rhubarb, 1/2 cup demerara sugar, the ginger, and vanilla in a medium bowl. Set aside about 15 minutes for flavors to meld. Spoon half of mixture into a saucepan and cook over medium-high heat, stirring often, until slightly thickened, about 5 minutes. Stir into rhubarb in bowl and let cool completely.
Preheat oven to 375°. Roll a dough disk into a 10-in. circle on a lightly floured board. Cut 4 circles (each 5 in. wide; you can use a cereal bowl as a guide) and transfer to a rimmed baking sheet lined with parchment paper. Repeat with remaining disk and a second sheet, gathering dough and rerolling scraps as needed. Brush off any flour left on dough.
Using a slotted spoon, pile rhubarb (but not juices) in center of each circle. Gently pleat edges of dough over fruit; spoon juices into center. Lightly brush edges with cream and sprinkle all over with remaining 2 tbsp. demerara sugar.
Bake, switching baking sheet positions halfway through, until fruit is tender and bubbling, about 35 minutes. Immediately transfer crostatas with a wide spatula to a cooling rack. Serve warm or at room temperature.
*Find semolina and demerara sugar, a tan, coarse-grained sugar with a toffee nuance, in the baking aisle of well-stocked supermarkets.