Sprinkle 3/4 cup sugar evenly into a 10-inch cast-iron skillet; place over medium heat, and cook, stirring constantly with a wooden spoon, until sugar melts and becomes a light golden brown. Pour caramelized sugar into six 6-ounce custard cups or ramekins. Set aside.
Combine remaining sugar and eggs in a medium mixing bowl, beating well; gradually add milk, stirring constantly. Stir in vanilla, and pour into prepared custard cups.
Place custard cups in a 13- x 9- x 2-inch baking pan; pour hot water into pan to a depth of 1 inch. Bake at 325° for 1 1/2 hours or until a knife inserted halfway between center and edge of custard comes out clean. Remove cups from water; cool. Invert custard onto individual dessert plates. Serve warm or chilled.