For the Vanilla Brûlée Syrup, mix 1/4 cup of the sugar and 1 tablespoon of the water in small heavy-bottomed saucepan. Cook on medium heat 5 minutes or until the syrup is a dark caramel color, stirring occasionally. Remove from heat. Slowly add remaining 1/2 cup water. Once the mixture is no longer steaming, add remaining 1/2 cup sugar. Cook and stir on medium heat until sugar is dissolved. Stir in vanilla. Set aside.
For the Peach Brûlée, toss peach wedges and sugar in medium bowl until well coated. Arrange peaches in single layer on large shallow foil-lined baking pan. Brûlée or broil one side of each peach wedge 3 to 5 minutes or until lightly browned. Set aside.
For the Peach and Vanilla Brûlée Cocktail, mix 4 of the brûléed peach wedges, peach schnapps and lemon juice in large cocktail shaker. Top with ice and heavy cream. Cover and shake until well mixed and chilled. Strain into 4 cocktail glasses. Garnish the rim of each glass with a remaining brûléed peach wedge. Slowly pour about 1/4 cup of the Vanilla Brûlée Syrup over each peach wedge and into the glass. (The syrup will sink to the bottom of the glass.)