1. Preheat oven to 325°.
2. To prepare crust, wrap heavy-duty aluminum foil around the bottom and sides of a 10-inch springform pan. Lightly coat pan with cooking spray.
3. Place graham crackers and 2 tablespoons pistachios in a food processor; process until finely ground. Add oil; process until moist. Firmly press crumb mixture into bottom and 1 inch up sides of prepared pan.
4. To prepare filling, combine 2 cups diced nectarine and 1 tablespoon sugar in a small saucepan. Cover and cook over low heat 5 minutes or until sugar dissolves. Uncover and cook 5 minutes or until mixture thickens. Cool.
5. Place cottage cheese in food processor; process until smooth. Add nectarine mixture, remaining 1 cup sugar, cream cheese, and cornstarch; process until smooth. Add sour cream, vanilla, egg whites, and egg; pulse just until combined. Pour cheese mixture into prepared pan. Place pan in a shallow roasting pan; add enough boiling water to come halfway up sides of pan.
6. Bake at 325° for 50 minutes or until center barely moves when pan is touched. Turn oven off and open oven door; cool cheesecake in oven 1 hour. Remove cheesecake from roasting pan; run a knife around outside edge. Discard foil. Cool completely on wire rack. Cover and chill at least 8 hours.
7. To prepare brittle, coat a baking sheet with cooking spray. Combine 1/2 cup sugar and 1/3 cup water in a small saucepan over medium-high heat; bring to a boil. Cook 1 minute or until sugar dissolves. Continue cooking 4 minutes or until golden (do not stir). Remove from heat; carefully stir in 1/4 cup chopped pistachios. Quickly spread mixture in a thin layer onto prepared baking sheet. Cool completely; break into small pieces. Sprinkle brittle around edge of cheesecake.
8. To prepare sauce, combine 2 cups chopped nectarine, 2 tablespoons sugar, and juice in a blender; process until smooth. Serve with cheesecake.