Beat cream cheese with an electric mixer until fluffy, adding eggs one at a time, then vanilla and sugar. Beat on low speed until incorporated, scraping down bowl as needed.

Place springform pan with crust in a shallow baking pan. Pour filling into crust and bake in the pan for 45 minutes, or until set 3 inches from the edge but still wobbly in the center. Allow to stand for 5 minutes. Keep oven on.

Mix together sour cream, sugar, and vanilla. Drop spoonfuls around the edge of the cake and spread gently over the center. Bake with topping for 10 minutes.

Run a knife around the edge of the cake to loosen. Cool completely in springform pan on a rack. Chill for at least 6 hours. Remove side of pan and transfer cake to a plate. Bring to room temperature before serving.