Preheat oven to 350°F. Stir together granulated sugar and 1/4 cup water in a medium saucepan. Using a pastry brush dipped in water, brush off any sugar clinging to sides of pan. Bring mixture to a boil over high, taking care not to jostle pan. Continue boiling, undisturbed, until syrup starts to turn a slightly pale brown, 6 to 8 minutes; gently swirl pan to even out caramelization. Continue boiling over high, swirling pan often, until syrup turns golden brown, about 2 minutes. Reduce heat to medium; carefully pour in corn syrup. (Mixture will sputter a bit and turn clumpy.) Cook, whisking occasionally, until clumps have completely melted, 1 to 2 minutes. Remove from heat; whisk in butter until melted.
Whisk together eggs, vanilla, and salt in a medium-size heatproof bowl. Gradually pour hot sugar mixture into egg mixture, whisking constantly, until completely combined. Add pecans; stir well to coat.
Pour pecan mixture into cooled pie shell. Bake pie in preheated oven until top is starting to set but filling is still jiggly, 15 to 20 minutes. Remove from oven; let cool 5 minutes.
While the pecan filling cools, make the pumpkin filling: Whisk together pumpkin, vanilla, ginger, cinnamon, salt, and nutmeg in a small saucepan. Cook over high, whisking constantly, until mixture reduces slightly and starts to darken in color, 3 to 4 minutes. Remove from heat; whisk in heavy cream and granulated sugar. Whisk in eggs until well combined.
Pour pumpkin filling over warm pecan filling in pie shell; smooth top. (Cover edges of pie with aluminum foil to prevent overbrowning if crust is getting too dark.) Bake at 350°F until pumpkin filling puffs up and is set, 30 to 40 minutes. Remove from oven; let cool completely on a wire rack, about 2 hours. Gently press plastic wrap onto surface of pie; chill until cold, at least 6 hours or up to overnight.
Make the whipped cream: Beat heavy cream and powdered sugar with an electric mixer fitted with the whisk attachment on medium speed until stiff peaks form, 2 to 3 minutes. Transfer whipped cream to a piping bag fitted with a star tip. Pipe large stars over surface of chilled pie. Serve immediately, or chill, uncovered, up to 6 hours. Serve chilled.