1. Cook sugar in a saucepan over medium heat, stirring often, 5 to 7 minutes or until melted and medium-brown in color. Quickly pour into a 9-inch round cake pan with 2-inch sides. Using oven mitts, tilt cake pan to evenly coat bottom and seal edges.
2. Beat cream cheese at medium speed with an electric mixer in a large bowl 1 minute. (Do not overbeat.) Reduce speed to low; add eggs and egg yolks, and beat until well blended. Add sweetened condensed milk and next 3 ingredients, beating at low speed 1 minute. (Mixture should not be foamy and may be slightly lumpy.) Pour milk mixture over sugar in pan. Place cake pan in a roasting pan; add hot water halfway up sides of cake pan.
3. Bake at 325° for 1 hour or until edges are set. (The middle will not be set.) Remove from oven; remove cake pan from water, and place on a wire rack. Let cool completely. Cover and chill at least 8 hours. Run a knife around edges to loosen, and invert onto a serving platter.
Note: The flan will continue to set as it cools and will set completely when it is chilled.