Using kitchen shears or a paring knife, trim dough to a 1-inch overhang. With floured fingers, fold overhang under itself to form a rim; pinch between thumb and forefinger to form a uniform edge around rim of plate. Crimp with fingertips. Refrigerate pie shell until chilled, about 1 hour.
Preheat oven to 350 degrees. Line dough with aluminum foil, folding foil over rim of pie plate. Fill with dried beans or pie weights; bake until crust is firm, about 20 minutes. Carefully remove foil and beans. Cool crust completely before filling.
In a large bowl, whisk together eggs, brown sugar, vanilla, salt, pumpkin-pie spice, and pumpkin. Whisk in half-and-half. Pour mixture into cooled pie crust. Bake until set, about 1 hour. Cool on rack at room temperature, 1 hour, then refrigerate to cool completely.
Make whipped cream: In a medium bowl, with an electric mixer, beat cream, maple syrup, and granulated sugar until soft peaks form.
If making in advance, cover cooled pie in plastic, and refrigerate up to 2 days. When refrigerating pie, cover first with a paper towel, then plastic wrap. The towel absorbs moisture and keeps the surface free of droplets.