Preheat oven to 350 degrees.

In the work bowl of a food processor, grind cinnamon twists into crumbs. Combine with melted butter. Press firmly into the bottom of a 9-inch springform pan; set aside.

In a medium bowl, combine 3/4 cup sugar, pumpkin, 3 egg yolks, cinnamon, mace, ginger, and salt. Mix well; set aside.

In another bowl, beat cream cheese at medium speed with an electric mixer until light and fluffy. Gradually add remaining 1/4 cup plus 2 tablespoons sugar; beat well. Add whole egg, remaining egg yolk, and whipping cream, beating well. Add cornstarch, vanilla, and lemon extract, beating until smooth. Add pumpkin mixture and beat well. Pour batter into prepared pan. Sprinkle cake doughnut pieces over batter.

Bake for 50 minutes. Do not overbake. Center may be soft but will firm up when chilled. Let cheesecake cool on a wire rack for 2 hours, then refrigerate for at least 2 hours before serving.

*Krispy Kreme Pumpkin Spice Cake Doughnuts are available only from September 30 through December 31 each year. When they are out of season, you can substitute 2 Krispy Kreme Glazed Sour Cream Doughnuts, crumbled and mixed with 1/2 teaspoon pumpkin-pie spice