Preheat an oven to 350 degrees F (175 degrees C). Grease the bottom and halfway up the sides of a 9 inch springform pan. Mix together the sugar, cornstarch, and flour and set aside.
Combine the cream cheese and cottage cheese; beat with an electric mixer at high speed until smooth and fluffy. Beat in the softened butter. Gradually add the sugar mixture, beating until combined. Add the eggs one at a time, blending well and scraping down the bowl after each addition. Stir in the lemon juice and vanilla and mix just until smooth.
Pour the batter into the prepared pan and bake for 1 hour and 10 minutes. Turn off the oven and let the cheesecake rest in the oven with the door closed for 2 hours. Remove and cool on a wire rack. Chill for 4 hours or overnight.