Arrange a rack to the lower-middle position in the oven and heat the oven to 425°F.

Roll out the pie crust and transfer it to a 9 ½ to 10-inch deep dish pie pan. Crimp the edges. Refrigerate for 30 minutes while the oven heats.

Line the pie crust with parchment paper or aluminum foil. 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 5 minutes more. Remove from the oven and keep near the stove.

Place 2 cups pumpkin purée, ½ cup granulated sugar, ½ cup packed light or dark brown sugar, ½ teaspoon kosher salt, 2 teaspoons ground cinnamon, 1 teaspoon ground ginger, ¼ teaspoon ground nutmeg, and ⅛ teaspoon ground cloves or allspice in a food processor fitted with the blade attachment or blender. Blend until the brown sugar is completely mixed in and the purée looks glossy.

Transfer the mixture to a large saucepan and place over medium-high heat. Stir frequently until you see wisps of steam rising from the purée, then stir continuously until the mixture is very steamy and 'plops' when you pause for a second. The mixture will also start to smell like spices and cooked pumpkin. Cook for no more than 5 minutes.

Remove the pan from the heat. Whisk in ¾ cup whole milk and ¾ cup heavy cream. To warm the 3 large 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 until smooth. Whisk in 1 teaspoon vanilla extract.

Place the partially baked pie crust on a parchment-lined baking sheet. 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.

Carefully transfer the baking sheet with the pie to the oven and immediately turn down the heat to 375°F. Bake until the pie is puffed in the middle but still jiggles when you gently shake the pan, 50 to 60 minutes. 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 aluminum foil if it becomes deep brown.

Let the pie cool to room temperature on a wire cooling rack before serving — it will continue to set as it cools.