In a mixing bowl, combine the cold butter, shortening, flour, and salt. Use your fingertips or a pastry blender to work the fats into the flour until it looks crumbly, almost like coarse sand. Pinching the fat between your fingers instead of mashing it creates those flaky layers you want in the finished crust.
Sprinkle the ice-cold water over the flour mixture and stir gently with a fork until it starts to come together. Press it into a disk shape, wrap it tightly, and refrigerate for about 20 minutes. This resting time keeps the butter firm, which is what gives you a flaky crust instead of a tough one.
While the dough chills, preheat your oven to 400°F. In a separate bowl, whisk together the sugar, cinnamon, ginger, nutmeg, cloves, salt, pumpkin puree, milk, and one egg until completely smooth. Set the filling aside so the flavors have a moment to meld together.
Flour your work surface and roll the chilled dough into a rough circle, about nine inches across. Use a 3 to 4-inch round cookie cutter to cut out circles, then gently press each one into the cups of your muffin pan, fluting the edges with your fingers if you like a decorative touch.
Spoon the pumpkin filling evenly into each crust-lined cup, filling them almost to the top without overflowing. Brush the beaten egg lightly along the exposed crust edges. This little step is what gives the finished pies that bakery-style golden shine.
Bake the pies at 400°F for 10 minutes, then lower the oven temperature to 325°F and continue baking for another 10 minutes. This two-stage bake sets the crust quickly before gently finishing the custard filling so it doesn't crack or puff up too much.
Let the pies cool fully in the pan before attempting to remove them, since the filling needs time to firm up. Run a thin knife around the edge of each pie to loosen it, then lift them out carefully onto a cooling rack or serving plate.