Make the dough: Pulse flour, sugar, and salt in a food processor until combined. Add butter and shortening, and process just until mixture resembles coarse meal. Pour in ice water, pulsing just until dough comes together. Divide dough in half. Shape each half into a disk, and wrap in plastic. Refrigerate for at least 1 hour (or overnight).
Make the vegetable filling. Preheat oven to 425 degrees. Toss together carrot, parsnip, garlic, oil, 1 teaspoon salt, and the pepper in a small roasting pan or baking dish. Roast until golden and tender, about 30 minutes. Squeeze garlic from skins, and toss with vegetable mixture; discard skins.
Heat butter in a skillet over medium-high heat. Add onion, and cook until translucent, about 1 minute. Add chard and remaining teaspoon salt, and cook until soft, about 4 minutes. Drain, and toss with vegetable mixture. Remove from heat, and let cool.
Reduce oven temperature to 375 degrees. On a lightly floured work surface, roll out one disk of dough to 1/8 inch thick. Using a 4-inch leaf-cutter, cut out 12 leaves. Place on parchment-lined baking sheets. Place a heaping tablespoon of vegetable filling on each leaf.
Whisk together egg yolk and cream. Roll out remaining dough to 1/8 inch thick. Cut out 12 more leaves. Using a small paring knife, etch veins on leaves. Brush edges of each filled leaf with egg wash; top with a veined leaf. Press edges together to seal. Brush tops with egg wash, and refrigerate for 30 minutes.
Bake pies until golden brown, about 30 minutes. Serve warm.
The dough and fillings for these small pies can be made a day ahead of time and stored in the refrigerator until ready to use.