Preheat oven to 375° (convection not recommended). Peel sweet potatoes and cut in half lengthwise. Place in a 9- by 13-inch baking pan and brush with melted butter. Bake until potatoes are soft when pressed, 45 to 55 minutes.
Meanwhile, prepare crust. Bake in same oven with potatoes until lightly browned all over, 10 to 12 minutes.
Scrape any charred spots off potatoes, then cut potatoes into chunks. Whirl in a food processor or mash in a bowl with lemon juice until smooth. Reserve 1 cup; save any extra for another use.
Reduce oven temperature to 325°. In a bowl, with a mixer on high speed, beat cream cheese until fluffy. Gradually beat in granulated and brown sugars, scraping down sides of bowl occasionally, until mixture is well blended and smooth. Beat in eggs, one at a time, until blended. Add reserved sweet potato mixture, the whipping cream, sour cream, maple syrup, cinnamon, nutmeg, and ginger. Mix on low speed until well blended.
Wrap bottom of cheesecake pan with heavy-duty foil, pressing it up the sides. Pour batter over crust. Put cheesecake pan in a 12- by 15-inch roasting pan at least 2 inches deep. Set pans in oven and pour enough boiling water into roasting pan to come halfway up sides of cheesecake pan.
Bake until cake barely jiggles in the center when gently shaken, about 55 minutes. Remove pans from oven. Lift cheesecake pan from roasting pan and let cool completely on a rack, about 1 hour, then chill until cold, at least 1 1/2 hours, or up to 3 days (cover once cold).
Up to 6 hours before serving, cut around inside of pan rim to release cake; remove rim. With a pastry bag, pipe dollops of maple cream onto cake. Or serve maple cream separately, to spoon onto each wedge.
Pecan Crust: Whirl 1/4 cup coarsely chopped pecans in a blender until finely ground; you should have 1/4 cup. In a bowl, mix pecans, 1 1/4 cups fine graham cracker crumbs, 2 tablespoons sugar, and 5 tablespoons melted butter. Pour into a 9-inch cheesecake pan with removable rim (2 1/4 in. tall). Press mixture evenly over bottom of pan.
Maple Cream: In a bowl, with a mixer on high speed, beat 3/4 cup whipping cream until stiff peaks form. On low speed, beat in 1/4 cup maple syrup just until blended.