In a medium saucepan, combine the cranberries and 3/4 cup water. Bring to a boil, stirring occasionally, about 12 minutes. Remove from the heat and stir in 1/3 cup of the sugar until dissolved. Strain the mixture through a sieve and let the puree cool completely.
Preheat the oven to 275 degrees. Butter and flour a 9 by 2-3/4 inch spring form pan.
In a large bowl, using an electric mixer, beat the cream cheese with the remaining 1 cup plus 2 tablespoons sugar and the vanilla at low speed until smooth. Beat in the eggs one at a time, beating until just blended. Stir in the sour cream.
Spoon half of the cream cheese mixture into the prepared pan. Drop 8 or 9 rounded teaspoons of the cranberry puree randomly over the top. Spoon half of the remaining cheesecake mixture evenly over the first layer and dot with half of the remaining puree. Repeat with the remaining cheesecake mixture and puree. Using a knife swirl the
cranberries into the batter.
Place the pan on a baking sheet and bake in the lower part of the oven for 1 hour. Turn the oven off and leave the cheesecake in for 1 hour longer. Transfer the cake to a rack and let cook to room temperature. Cover and refrigerate overnight before serving.