Heat oven to 350°F. Peel and core apple. Cut into thin slices; cut each slice in half crosswise. Arrange in bottoms of 6 (6-oz) ungreased custard cups.
In heavy 2-quart saucepan, mix 3/4 cup sugar and the water. With pastry brush dipped in water, wash any sugar off inside of pan. Without stirring, cook over medium-high heat 5 to 6 minutes or until mixture begins to turn amber in color. Gently swirl pan as mixture darkens to golden brown (watch carefully, as mixture can burn in seconds). Immediately remove from heat. Carefully pour over apples in custard cups. Place custard cups in 13x9-inch pan.
In medium bowl, beat eggs, egg yolks, 1/2 cup sugar and the vanilla with electric mixer on medium speed until well combined. Gradually beat in whipping cream until blended. Carefully pour over caramel mixture in cups.
Place pan with cups in oven; pour hot water into pan until about halfway up sides of custard cups. Bake 50 to 60 minutes or until knife inserted in center comes out clean (apples may float to top). Remove cups from water; place on wire rack. Cool 30 minutes. Refrigerate until completely chilled, about 1 hour.
To unmold, run thin knife around inside edge of each cup. Place bottom of cup in hot water for 30 to 60 seconds to loosen caramel. Unmold onto individual dessert plates. Store in refrigerator.