Preheat oven to 325° F. In a large mixing bowl, beat the cream cheese until smooth, about 1 minute. Beat in the eggs one at a time. Add 1 cup of the sugar and 1 teaspoon of the vanilla and mix until well combined. Pour the batter into the crust and bake until set, 45 to 50 minutes. In a small bowl, whisk together the sour cream and the remaining sugar and vanilla. Pour the mixture over the cheesecake, spreading it to the edge. Bake 5 minutes. Cool and refrigerate overnight before serving.