Flourless Chocolate Cake: Bring water and 1 qt. sugar to boil in medium saucepan on medium heat; cook until sugar is dissolved, stirring constantly. Remove from heat. Add chocolates; stir until melted.
Beat eggs and remaining sugar in 6-qt. bowl of mixer fitted with paddle attachment 3 min. or until well blended. Whisk in chocolate mixture, butter and vanilla.
Cheesecake: Beat cream cheese in 6-qt. bowl of mixer fitted with paddle attachment on medium speed 1 min. Add sugar; beat 2 min. or until well blended. Add cream and vanilla; mix well. Gradually add whole eggs and yolks, beating on low speed after each addition just until blended.
Butter 40 each 3-inch cake rings. Place in parchment paper-lined full-sheet pan. Add 2 slightly rounded #20 scoops (about 4.7 oz.) of the chocolate cake batter to each ring. Top each with #20 scoop (about 1.7 oz.) of the cheesecake batter, pressing scoop gently into cake batter so that it rises around the cheesecake batter.
Place full steamtable pan filled with hot water on bottom rack of 325ºF standard oven. Place pan of cheesecakes on top rack. Bake 25 to 30 min. or until cakes start to puff over tops of rings. Cool cakes completely in rings in pan.
Dip paring knife in warm water; run around edge of each cake in cake ring. Carefully remove cake rings. Use spatula to place 1 cake on each cookie. Wrap individually in plastic wrap. Refrigerate until ready to serve.