For the tarts:

Make the dough: Combine the corn and all-purpose flours plus the cornmeal, sugar and salt in  ingredients in the bowl of a food processor. Add the butter and pulse in short bursts, until the mixture resembles coarse cornmeal. Add the heavy cream and egg yolks and pulse until combined; it will look crumbly but it will become one mass when kneaded together.

Shape the tarts: Divide the dough into 10 equal pieces. Lightly flour a work surface and using the heel of your hand, flatten the dough into a rough circle. Continue flattening until it is approximately 4 inches in diameter. Try to work quickly, so the dough doesn’t get too warm and soft, making it harder to handle. For more elegant edges, gently flatten the outer edge of the circle with your fingertips, making it thinner than the rest of the dough.

Make the Rhubarb Vanilla Compote:

Leave 1½ cups of the rhubarb aside and put 3 cups into a large, heavy-bottomed pot. Add the brown sugar, vanilla bean seeds and pod and turn the heat to medium low. (You want to start at a low temperature to encourage the rhubarb to release its liquid. Unlike most compotes, this one adds no water.) 

Cook the rhubarb mixture, covered, for about 15 minutes, or until the mixture is saucy. Remove the cover and increase the heat to medium, cooking an additional 15 to 17 minutes, or until the rhubarb is completely broken down and thick enough that a spoon leaves a trail at the bottom of the pan. 

Discard your vanilla bean pod and add the reserved rhubarb to the compote. Pour the compote out onto a large plate to cool.

Do ahead tip: This compote keeps for one week in the fridge. It can also be used to fill pies, crisps and cobblers.

Add the compote: Spoon 3 tablespoons of the Rhubarb Vanilla Compote into the center of the dough. Fold the edge of the dough toward the compote and up, to create a ruffled edge; continue around the perimeter, letting the ruffles be their bad irregular selves. Slide a bench scraper or spatula under the tart and transfer it to a parchment-lined baking sheet. Continue with the remaining dough. Freeze the tarts on their tray for at least 1 hour or up to 2 weeks, wrapped tightly in plastic.

Bake the tarts: Preheat over to 375°F. Bake tarts, still frozen, for about 35 minutes or until the edges of the tarts are brown and the rhubarb is bubbling and thick. Serve warm or at room temperature.