Preheat the oven to 350°F (180°C).
On a floured surface, roll out the pie crust to a ¼-inch (6-mm) thick round, then line a 9-inch (23-cm) pie tin with it and crimp the edges. Place a piece of parchment on the pie crust, fill with pie weights, and bake for 20 minutes.
Remove the parchment and pie weights and bake for about 10 minutes more until the bottom is dry. Remove from the oven and set aside.
To Make the Pumpkin Layer: Whisk together the pumpkin puree, granulated sugar, egg, and pumpkin pie spice in a medium bowl until smooth. Set aside.
To Make the Pecan Layer: In a medium bowl, mix the corn syrup, brown sugar, eggs, butter, and vanilla extract until blended, then fold in the pecans. Set aside.
To Assemble and Bake: First, pour the pumpkin layer into the crust, then top with the pecan layer.
Place the pie on a baking sheet to catch any drips, and bake for about 45 minutes, until the edges are set but the center still jiggles slightly. (If the crust starts to overbrown before the filling is set, cover it with a ring of foil for the remainder of the baking time.)
Let cool to room temperature, then refrigerate for at least 3 hours or until cold before serving.
Serve with a dollop of freshly whipped cream if you wish! Store well covered in the refrigerator for up to 2 days.