Pierce sweet potatoes with a fork and microwave for 8–10 minutes, flipping halfway, until soft.
Bake at 400°F (200°C) for 45–60 minutes or boil until tender. Let cool, peel off the skins, and mash until smooth.
In a large bowl, mix mashed sweet potatoes with granulated sugar, brown sugar, and melted butter until smooth.
Slowly stir in evaporated milk until well blended. Beat in eggs one at a time, then mix in vanilla extract.
Preheat oven to 375°F (190°C). Place pie crust in a 9-inch pie dish. Pour in the sweet potato filling and smooth the top with a spatula.
Bake for 50–60 minutes, until the filling is set and the crust is golden.
If the crust browns too quickly, cover the edges with foil. The center should look firm and slightly puffed.
Cool completely on a wire rack to help the pie set. Slice and serve warm or chilled. Top with whipped cream or vanilla ice cream if desired.