In a large mixing bowl, whisk together the brown sugar, cornstarch, pumpkin pie spice, cinnamon, nutmeg and salt. Add 1-2 tablespoons of the non-dairy milk, stirring until a thick paste forms. Slowly pour in the remaining non-dairy milk, whisking continuously to prevent clumping. Stir in the pumpkin puree, maple syrup and vanilla extract.
Place your 9" pie dough in a pie dish. If you're using the oil pie crust recipe, I recommend avoiding any fancy edges. It'll be easiest if you just make a flat, simple edge.
Pour the pumpkin mixture into the unbaked pie crust. Smooth into an even layer with a spatula. Place the pie on the middle rack of the oven. Bake at 375F for 45-55 minutes. Cover edges with tin foil or a pie shield if baking too quickly.
The pie is cooked when the edges are firm and the center is still a little jiggly, but not liquid. Remove from the oven and let cool to room temperature, about an hour. After cool, refrigerate for 3-4 hours, until chilled through.
Once chilled, slice and enjoy with non-dairy whipped topping and a drizzle of maple syrup.
The pie takes longer to bake and set depending on the dish you use. It is done in about 50 minutes using a thin metal pie dish (the disposable kind). Ceramic or glass may take 5-10 minutes longer.