1. Heat oven to 400 degrees F. Line a baking pan with foil. Prick sweet potatoes with a fork; arrange on prepared pan. Bake 60 to 70 minutes, until very soft. Cool; cut in half and scoop out flesh. Mash and set aside (you should have 1-1/4 cups).
2. Meanwhile, for pastry, combine flour and sugar in a large bowl. With pastry blender or 2 knives, cut in butter until mixture resembles fine crumbs. Beat 1 egg and 1 yolk together in a cup; add to flour mixture, tossing with a fork until mixture begins to hold together. On lightly floured surface, shape pastry into a ball, then flatten into a disk. Wrap and refrigerate 1 hour.
3. On a lightly floured surface with floured rolling pin, roll pastry to an 11-inch circle, 1/4 inch thick. Using the bottom of 9-inch springform pan as a guide, cut pastry into a 9-inch circle. Lightly butter bottom of pan, then transfer pastry to pan. Press edge of circle against side of pan. Bake until golden, 20 to 23 minutes. Cool on wire rack.
4. Reduce oven temperature to 250 degrees F. Combine flour, cinnamon, ginger, and nutmeg in a cup.
5. Process ricotta in food processor until very smooth, 1 minute. Transfer to large mixer bowl. Beat in cream cheese and granulated and brown sugars at medium speed until smooth and fluffy, scraping down sides of bowl with a rubber spatula. Beat in sweet potatoes. At low speed, add 2 eggs and 2 egg yolks, one at a time. Add flour-spice mixture and beat just until smooth. Pour filling into prepared pan. Bake cheesecake until firm, 1 hour 20 minutes. Cool on wire rack. Cover and refrigerate overnight. To serve, run a small knife around the side of pan, then detach ring. Makes 12 servings.