Preheat oven to 325°. Line bottom of a 9-in. springform pan with parchment paper; 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 40-50 minutes or until center is set. 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 two greased 9-in. round baking pans with parchment paper; 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 30-35 minutes or until a toothpick inserted in center comes out clean. Cool in pans 10 minutes before removing to wire racks; remove paper. 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 one 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.
Make patties: In a large bowl, combine beef, egg, bread crumbs, ketchup, Worcestershire sauce and garlic. Season with salt and pepper and form into 4 oval patties.
In a large skillet over medium heat, heat oil. Sear both sides of the patties until a crust forms, about 5 minutes per side. Remove onto a plate.
Make gravy: Wipe out skillet and add butter. Add onions and thyme and stir until onion becomes translucent. Add mushrooms and cook until browned and tender, about 4 minutes. Sprinkle onions and mushrooms with flour, and stir until they are fully coated. Cook another 2 minutes, then add Worcestershire sauce, tomato paste, and beef stock. Stir to combine and season with salt and pepper.
Bring the gravy to a simmer and return the patties to the skillet. Cover and cook for 10 to 15 more minutes, until the patties are done and the sauce has thickened. Plate the patties and top with more gravy. Serve.