Combine first 4 ingredients in a Dutch oven; set aside until syrup forms. Bring peach mixture to a boil; reduce heat to low, and cook 10 minutes or until tender. Remove from heat, add vanilla and butter, stir until butter melts.
Roll half of pastry to 1/8-inch thickness on a lightly floured surface; cut into an 8-inch square. Spoon half of peaches into a lightly buttered 8-inch square pan; top with pastry square.Bake at 475F for 12 minutes or until lightly browned. Spoon remaining peaches over baked pastry square.
Roll remaining pastry to 1/8-inch thickness, and cut into 1-inch strips;arrange in lattice design over peaches. Bake an additional 15 to 18 minutes or until browned. Spoon into serving bowls, and top each with a scoop of ice cream.