Prick the sweet potatoes with a fork and roast them on a baking sheet until very tender, about 70 minutes.
When ready to bake the pie, preheat the oven to 400°F. Set a rimmed baking sheet in the oven to preheat along with the oven.
Remove the skin from the potatoes and put them in a mixing bowl. Mash very well with a potato masher.
In a saucepan, melt the butter. Add the sugar to the melted butter and stir to let it dissolve a bit.
Add the butter & sugar mixture to the potatoes, followed by the milk and the eggs and beat with a whisk until smooth. Whisk in the remaining ingredients (the filling will be quite liquid) and pour into an unbaked pie shell.
Carefully transfer the pie to the heated shallow baking sheet and bake on the bottom rack of the oven until the filling is just set, about 40 minutes. Transfer the pie to a rack to cool.