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