How to Make It
In a food processor, combine the flour, cornmeal, salt and chives and process to blend. Add the butter and pulse a few times until the pieces are the size of small peas. Add the shortening and pulse a few times. Sprinkle the ice water over the mixture and pulse until the dough barely comes together. Scrape the dough onto a lightly floured work surface and knead to form a ball. Flatten the ball into a disk, wrap in plastic and refrigerate for 1 hour, or until firm.
Remove the favas from the pod. Fill a large skillet halfway with salted water and bring to a boil. Add the favas and blanch. Using a slotted spoon, transfer the favas to a baking sheet. Let cool slightly, then peel. Add the asparagus to the boiling water and cook until just tender, about 3 minutes. Drain and transfer to the baking sheet to cool. Cut the asparagus into 1-inch pieces.
Wipe out the skillet and heat the 3 tablespoons of olive oil. Add the garlic and cook over low heat, stirring, until golden, 1 1/2 minutes. Add the scallions and cook over moderate heat until softened, 2 minutes. Add the favas and asparagus and cook until heated through, about 2 minutes. Season with salt and pepper. Let cool.
Preheat the oven to 400°. On a floured work surface, roll out the pastry to a 14-inch round, about 1/8 inch thick. Roll the pastry around the rolling pin and carefully transfer to a parchment paperlined baking sheet. Scrape the vegetable mixture into the center of the pastry, leaving a 1 1/2-inch border all around. Fold the edges up over the filling and scatter Gruyère on top. Brush the edges with olive oil. Bake the tart on the bottom rack of the oven for about 30 minutes, until the crust is crisp on the bottom and golden brown. Let the tart cool to warm. Cut into wedges and serve.