Preheat oven to 450 F/230 C. Place sweet potatoes on a baking sheet lined with foil and bake for about 1 hour or until a skewer easily slides into flesh. Remove from oven and let them cool slightly then peel off the skins and discard skins.
Place the sweet potatoes in a food processor and process until smooth. Let them cool to room temperature, at least 1 hour.
Lightly grease a 9-inch/23 cm springform pan and line the bottom with non-stick parchment.
Preheat oven to 425 F/220 C.
Beat cream cheese, sugar and brown sugar in a sturdy mixer until mixture is very smooth, about 3-5 minutes. With mixer still running, add 2 cups of the sweet potatoes gradually and beat until fully incorporated.
Add the eggs, one at a time, beating well after each addition.
With mixer on low speed, add the cream, sour cream, salt and vanilla. Turn off mixer and sift in the flour, cinnamon, ginger and nutmeg. Turn on mixer to low speed and beat until just incorporated. Fold a few strokes by hand making sure to scrape the bottom of the bowl to make sure everything is mixed in.
Pour mixture into prepared pan and smooth the surface. Place pan on a tray and bake for 55-65 minutes. Top will be deeply brown (and resemble chocolate) and will have a slight wiggle in the center. Transfer to a rack and cool at least 1 1/2 hours.