Poke the sweet potatoes with a fork and wrap them in foil. Bake at 400℉ (205℃) for 45-50 minutes until the potatoes are soft. You may need more cooking time depending on the size of your sweet potatoes.
Cool, remove the foil, and peel the sweet potatoes.
Place the sweet potatoes in a large bowl. Using a potato matcher, match them until partly smooth.
Add all the other ingredients: sugars, eggs, milk, butter, cinnamon, nutmeg, allspice, salt, and vanilla extract. Mix using a hand mixer until thoroughly combined.
Pour the sweet potato pie mixture into the baked pie crust, leaving ½-¾" between the filling and the top of the pie shell.
Bake at 450℉ (230℃) for 10 minutes, lower the temperature to 350℉ (175℃), and bake for 35-40 minutes until set.
Once the pie is done, turn the oven off and crack the oven door open. You'll notice that the top of the pie will puff up during baking but return to a flat as it cools. Cool the pie completely in the oven with the door open so it doesn't crack.
Once fully cooled, cut into slices and serve with homemade whipped cream or your choice of vanilla or pecan praline ice cream!