To cut clean slices, dip a sharp knife into water before each cut.
Preheat the oven to 300 degrees. Grease a 10-inch spring-form pan with butter, shortening or cooking spray.
Blend the graham crackers and 1/2 tablespoon sugar by crumbling in a zip-tight bag until finely crushed. Add the melted butter to the graham crackers. Press the mixture into the bottom of the spring-form pan.
bring the cream cheese, cottage cheese, sour cream and eggs to room temperature for (approximately 1 hour) before mixing. Place the cottage cheese in a blender on the lowest speed just until smooth (try not to over-blend).
Soften two 8-ounce packages + 1/4 cup (18 ounces total) of cream cheese with a mixer on medium-low speed for 30 seconds, taking care not to incorporate too much air.
Add 3/4 cup plus 3 tablespoons of sugar and a pinch of salt and mix for 30 seconds. Gradually add the egg yolks and then the whole eggs one at a time to the cream cheese mixture, scraping down the sides of the bowl three times during additions to prevent lumps. Stir in the cottage cheese, sour cream and vanilla extract. Pour the filling over the prepared crust.
Bake for approximately 50 minutes or until the center remains slightly loose, but the sides have fully set up. Cool to room temperature. Cover and place in the refrigerator to cool completely before removing from pan.