Once you add the eggs to the cheesecake batter, pulse just until combined. Incorporating too much air at that stage can cause the cheesecake to puff up as it bakes and sink as it cools, leaving a cracked or sunken appearance.
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.
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.
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.
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.
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.
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.
To prepare sauce, combine 2 cups chopped nectarine, 2 tablespoons sugar, and juice in a blender; process until smooth. Serve with cheesecake.