Preheat oven to 350°.
Prepare brownie mix according to package directions using yogurt and 1 egg white. Spread batter into an 8-inch square baking pan coated with cooking spray. Bake at 350° for 35 to 40 minutes or until done. Cool completely in pan on a wire rack.
Reduce oven temperature to 325°.
Combine cottage cheese and cream cheese in a food processor, and process 2 minutes or until smooth. Add sugar, cocoa, flour, and salt. Process 30 seconds or just until blended, scraping down sides of bowl if needed.
Combine coffee granules and hot water. Stir in raspberry spread and melted chocolate. Add raspberry mixture, remaining egg white, eggs, and vanilla to cream cheese mixture in processor; process just until combined.
Crumble brownie evenly into a 9-inch springform pan coated with cooking spray. Press brownie firmly to form a compact crust.
Pour batter over crust. Bake at 325° for 1 hour and 20 minutes or until almost set. Turn off oven; leave cake in oven 1 hour. Remove from oven; run a knife around edge. Cool completely in pan on a wire rack. Cover and chill at least 8 hours.