Position a rack in the bottom third of your oven. Preheat the oven to 350°F.
In a small saucepan over medium heat, combine the ginger, crushed cinnamon sticks, heavy cream, and milk to scalding. Remove from the heat, cover, and let steep for 10 minutes. Return the saucepan to medium heat and bring back to scalding.
Meanwhile, in a medium bowl, whisk together the eggs, egg yolks, sugar, and salt until pale yellow. Whisk in the hot ginger cream, little by little, until combined. Strain the mixture into a clean pitcher and set aside.
In a separate bowl, briefly whisk the pumpkin puree until smooth. Slowly whisk in the ginger custard until incorporated.
Pour the pumpkin custard into the prebaked pie shell. Bake for 60 to 70 minutes, or until set-the center is no longer jiggly. Remove to a wire rack to cool.
The pie keeps tightly wrapped in plastic wrap at room temperature overnight. For longer storage, it keeps wrapped in plastic wrap in the refrigerator for up to 3 days (the crust will suffer slightly from the chilling).
All-Butter Pie Dough
(makes enough for 1 double-sided pie or 2 single crust 10-inch pies)
In a large bowl, whisk together the flour, sugar, baking powder, and salt to combine.
Add the butter pieces, tossing your fingers to coat each cube in the flour. Using a pastry blender, cut the butter into the flour until the size of large peas.
Sprinkle 6 tablespoons of the water over the mixture and toss with a fork. The dough should hold together when you squeeze it in your hand. If it is too dry, add the rest of the water (or more is absolutely necessary).
Turn the dough out onto a lightly floured work surface. Pat it together into one piece. Divide the dough into two equal parts, flatten each into a round disk, and the wrap tightly with plastic wrap. Refrigerate for at least 30 minutes before rolling.