Preheat oven to 325°. Line bottom of a 9-in. springform pan with parchment; grease paper.
In a large bowl, beat cream cheese and sugar until smooth. Beat in sour cream, flour and vanilla. Add eggs; beat on low speed just until blended. Pour into prepared pan. Place on a baking sheet.
Bake until center is set, 40-50 minutes. Cool on a wire rack 10 minutes. Loosen sides from pan with a knife. Cool 1 hour longer. Refrigerate until ready to assemble, covering when completely cooled.
For cake, increase oven setting to 350°. Line bottoms of 2 greased 9-in. round baking pans with parchment; grease paper.
In a large bowl, beat sugar, oil, buttermilk, eggs, food coloring, vinegar and vanilla until well blended. In another bowl, whisk flour, cocoa, baking soda and salt; gradually beat into sugar mixture.
Transfer to prepared pans. Bake until a toothpick inserted in center comes out clean, 30-35 minutes. Cool in pans 10 minutes before removing to wire racks; remove parchment. Cool completely.
For frosting, in a large bowl, beat cream cheese, butter and vanilla until smooth. Gradually beat in enough confectioners' sugar to reach desired consistency. Place 1 cake layer on a serving plate. Spread with 1 cup frosting. Carefully place cheesecake over frosting.
Spread cheesecake with another 1 cup frosting. Top with remaining cake layer. Frost top and sides of cake with remaining frosting. Refrigerate overnight before serving.