1. Make filling: Crush cardamom pods with the flat side of a chef's knife just to split. Melt 1 tablespoon butter in a small saucepan over medium heat; add crushed cardamom. Cook until fragrant, about 3 minutes. Add milk, cream, and ginger; bring to a simmer. Reduce heat to medium-low; cook 15 minutes. Remove from heat; let steep 30 minutes.

2. Melt remaining tablespoon butter in a large saute pan over medium heat. Add carrots; cook, stirring occasionally, 2 minutes. Stir in sugar and salt. Cover pan; cook until carrots are tender, about 8 minutes. Pour steeped milk through a sieve into pan with carrots; discard solids. Remove from heat; let cool slightly, about 5 minutes. Process carrot mixture in a food processor until completely smooth; transfer to a bowl.

3. Temper beaten eggs by whisking in up to 3/4 cup carrot mixture, 1/4 cup at a time, until eggs are warm to the touch. Pour warmed egg mixture into remaining carrot mixture; whisk until thoroughly combined. Let cool.

4. Make pies: Preheat oven to 375 degrees. Lightly sprinkle ground gingersnaps on a work surface to form a large circle about 18 inches in diameter. On crumbs, roll out pate brisee to 1/8 inch thick, turning occasionally to coat both sides.

5. Cut out eight 5-inch rounds from dough. Press rounds into eight 4-inch pie plates; trim excess. With a fork, crimp edges, and then prick bottom of dough all over. Refrigerate 30 minutes.

6. Line each pie shell with parchment paper or foil, and fill with pie weights or dried beans. Bake until golden brown, about 30 minutes. Transfer to a wire rack. Remove pie weights and parchment. Let shells cool completely.

7. Divide filling among shells. Bake until a cake tester comes out clean, 30 to 35 minutes. Serve pies warm with whipped cream dusted with ground cardamom.