Heat oven to 350°F. In a medium bowl, combine the ground gingersnaps and butter. Using a straight-sided dry measuring cup, press the mixture into the bottom and 2 inches up the side of a 9-inch springform pan.
Using an electric mixer, beat the cream cheese and 1 cup of the sugar until smooth. Beat in the eggs, one at a time. Beat in ½ cup of the sour cream and 1 teaspoon of the vanilla.
Pour the mixture into the crust and bake until just set, 40 to 45 minutes.
Meanwhile, in a small bowl, combine the remaining 1½ cups of sour cream, ¼ cup of sugar, and 1 teaspoon of vanilla. Spread over the hot cheesecake and bake until set, 3 to 5 minutes more. Let cool in the pan, then refrigerate for at least 4 hours. Run a knife around the edge of the cheesecake before unmolding.
Spread the preserves over the cheesecake before serving.