Place sweet potatoes in a large pot and cover with water. Bring to a boil, then reduce heat and simmer for 40–50 minutes until fork-tender. Drain, let cool for 10 minutes, then peel and mash until smooth.
In a large bowl, beat mashed sweet potatoes and softened butter until creamy. Add sugar, condensed milk, eggs, whole milk, vanilla, cinnamon, and nutmeg. Beat again until the mixture is smooth and thick but pourable.
Place the unbaked crust into a 9-inch pie plate. Pour in the sweet potato filling and smooth the top. Gently tap the plate on the counter to remove air bubbles.
Preheat oven to 350°F (175°C). Bake for 50–60 minutes, or until a toothpick inserted in the center comes out clean. The pie will puff slightly and settle as it cools.
Let the pie cool completely on a wire rack for at least 2 hours. Slice and serve plain or topped with whipped cream or vanilla ice cream.