Line a 9-inch pie pan withthe pastry and flute edges, then line pastry with foil. Partially fill with pie weights or dried beans.
Bake pie pastry in a 375° oven until edges are dry and barely golden, about 15 minutes. Remove from oven and carefully remove pie weights and foil. Reduce oven temperature to 350°.
Meanwhile, in a large bowl, whisk pumpkin, cream, eggs, brown sugar, granulated sugar, ground chiles, cinnamon, nutmeg, and salt until smooth.
Pour pumpkin mixture into hot pie crust and return pie to oven. Bake until center barely jiggles when shaken, about 45 minutes. Let cool to room temperature on a wire rack, at least 2 hours. Cut into wedges to serve.