Whisk 2 1/2 cups all-purpose flour and 1 teaspoon kosher salt in a large bowl.
Cut 6 Tablespoons chilled vegan butter and 2/3 cup chilled vegetable shortening into the flour mixture until coarse crumbs form.
Gradually add 1/2 cup ice water, 1 tablespoon at a time, mixing until the dough just comes together.
Roast 1.5 lbs sweet potatoes at 400°F (200°C) for 45-60 minutes until tender, then peel and mash.
Combine mashed sweet potatoes, 6 tablespoons melted vegan butter, 2/3 cup packed dark brown sugar, 1 1/2 cups canned full-fat coconut milk, and 1/4 cup cornstarch; whisk until smooth.
Roll out one disc of pie dough into a 12-inch circle and transfer to a 9-inch pie plate; pour in the sweet potato filling.
Bake at 375°F (190°C) for 50-60 minutes, covering edges with foil if needed, until the filling is set.
Cool completely on a wire rack before slicing and serving to allow the filling to fully set.