In the bowl of a stand mixer, beat together the butter, granulated sugar and brown sugar until creamed.
Add the eggs, one at a time, until they're fully incorporated. Stop the mixture and use a spatula to scrape any of the butter that's stuck to the bowl. Continue to beat until incorporated.
Add the evaporated milk, mashed sweet potatoes, vanilla bean paste, cinnamon, nutmeg and salt. Mix until everything is well-incorporated. {The mixture may look slightly curdled, but that's ok.}
Pour the mixture into the cooled crust and use a spatula to even out the top.
Place into the oven and lightly tent with a sheet of foil. Bake for about 30 minutes, then remove the foil, and bake for another 20 minutes. When done, the center will be mostly set {with a slight jiggle} and the mixture will have slightly puffed up.
Remove from oven and allow to cool for 20-30 minutes before cutting and serving, or cool completely then cover and chill in the refrigerator for several hours or overnight. Serve with a big scoop of vanilla ice cream.