1. Heat the oven to 425°F with a rack in the lower-middle position. Roll out the pie crust and transfer it to a 9-inch pie pan. Crimp the edges. Chill for 30 minutes while the oven heats.
2. Line the pie crust with parchment or aluminum foil and fill with pie weights (or dried beans). Bake until the edges just start to brown, 12 to 15 minutes. Remove the weights and lining, and bake for another 5 minutes. Remove from the oven and keep near the stove.
3. While the crust is baking, prepare the filling. Combine the pumpkin puree, granulated sugar, brown sugar, salt, and spices in the bowl of a food processor or blender. Blend continuously until the brown sugar is completely mixed in and the puree looks glossy.
4. Transfer the puree to a saucepan and set over medium-high heat. Stir frequently until you see wisps of steam rising from the puree, then stir continuously until the mixture is very steamy and
5. Off the heat, whisk the milk and cream into the pumpkin puree. To warm the eggs and ensure that they don't cook when you add them to the pumpkin mixture, whisk them together in a separate bowl, then whisk in a few spoonfuls of the warm pumpkin mixture. Slowly whisk the eggs into the saucepan with the pumpkin mixture. Whisk in the vanilla.
6. Place the partially-baked pie crust on a parchment-lined baking sheet and set it near the stove. Carefully pour the warm pumpkin mixture into the warm pie crust. If it looks like there's too much filling for the crust, stop when you come close to the edge of the crust.
7. Carefully transfer the baking sheet with the pie to the oven and immediately turn down the heat to 375°F. Bake for 50 to 60 minutes — until the pie is puffed in the middle, but still jiggles when you gently shake the pan. You'll also see small cracks form in the outer part of the pie and some bubbling around the edge. Check the pie every 15 minutes or so and cover the crust with a ring of foil when it becomes deep brown.
8. Let the pie cool before serving — it will continue to set as it cools. This pie can be baked a day or two ahead; wrap tightly in plastic wrap and refrigerate until ready to serve..