Preheat oven to 350 degrees F.
Combine the gingersnaps, oil, and 2 tablespoons brown sugar in the bowl of a food processor; pulse to form fine crumbs. Press the crumbs into the bottom and up the sides of a 9-inch pie plate. Bake until the crust is set and golden brown, 10 to 15 minutes. Let cool completely on a wire rack.
In a large bowl, stir together the pumpkin puree, vanilla, pumpkin pie spice and remaining 1/3 cup brown sugar until blended; stir in the frozen yogurt. Spread into the cooled pie crust and freeze until firm, about 3 hours. Wrap tightly in plastic to freeze up to 1 week.
When ready to serve, transfer the pie to the refrigerator to soften slightly, about 30 minutes. Top with Maple Whipped Cream, if desired.
Sprinkle the gelatin over the water in a medium bowl; let stand until absorbed, about 5 minutes. In a small saucepan, heat the milk until steaming. Whisk the hot milk into the gelatin to dissolve. Stir in the maple syrup and vanilla.
Place the bowl in a bowl of ice water and stir occasionally until just beginning to set around the edges, about 15 minutes. Using a hand-held mixer, beat the cold milk mixture on high until thick and fluffy, about 8 minutes. Spread on top of the frozen mousse pie; swirl like a meringue topping. Serve.
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