Place chocolate graham crackers in a food processor; process 30 seconds or until finely ground. Sprinkle crumbs over bottom of a 9-inch springform pan coated with cooking spray. Lightly coat crumbs with cooking spray. Wrap outside of pan with a double layer of foil.
Combine sugar, flour, and salt. Place cottage cheese and cream cheeses in a food processor; process 1 minute or until smooth. Add sugar mixture; process 1 minute or until smooth. Add vanilla, eggs, and egg white; process 1 minute or until well blended. Add half of chopped mints; pulse once to combine. Pour batter into prepared pan. Sprinkle remaining half of chopped mints evenly over batter. Place springform pan in a jelly-roll pan or large roasting pan; add hot water to pan to a depth of 1 inch.
Bake at 350° for 50 minutes or until cheesecake center barely moves when pan is touched. Remove the cheesecake from oven; cool in pan on a wire rack 5 minutes. Run a knife around outside edge. Cool to room temperature. Cover and chill at least 8 hours.