Preheat your oven to 400°F. Prepare your pie crust according to these directions. Once you've added the dough to the baking pan, poke holes in the bottom using a fork. Parbake (partially bake) the crust for 10 minutes. Let cool as you prepare the filling.
Reduce the oven temperature to 350°F.
Shake the can of coconut milk to evenly distribute the contents. Measure out 1 cup.
In a large bowl, whisk together the coconut milk, pumpkin pie, pumpkin pie spice, brown sugar, maple syrup, corn starch, and vanilla extract until smooth and creamy.
Pour the filling into the crust. Make sure the pie is even by smoothing out the filling with a spoon or silicone spatula.
Bake for 35-45 minutes on a lower rack. Cover the edges of the crust with foil or a pie crust shield after the first 15 minutes of baking to avoid burning.
You'll know your pie is done when it's firm on the edges, and jiggles (but doesn't look soupy) in the center. Let the pie cool on the counter for about an hour, and then let it set in the fridge for at least 3 hours.