Beat cream cheese and sugar together until well blended, then mix in sour cream and vanilla. Beat in eggs one at a time, then set aside.
Cake batter:
Sift dry ingredients together. Cream butter and sugar, then beat in eggs, then milk and vanilla. Stir in dry ingredients.
Grease and flour a deep 9-inch Pyrex pie plate, or a 9 x 9-inch square pan. Spread cake batter over bottom and sides, spreading much thinner on sides. Spoon cheesecake mixture over batter.
Bake at 325° for 40-45 minutes, until cheesecake is set. Spread with sour cream topping, then return to oven for another 5 minutes. Cool, then refrigerate at least 4 hours.