Heat a nonstick skillet over medium-low heat. Lightly butter the pan. Carefully dip the squares of cornbread into the egg mixture, gently shake off the excess, and place in the pan. (Don't allow the cornbread to soak in the mixture - just a quick dip.) Cook for 3 to 4 minutes on each side, adjusting the temperature to keep it from burning. (The sugar in the egg mixture will burn, so be cautious.) Repeat until all of the cornbread has been cooked, adding additional butter if necessary. Hold the other pieces in a warm oven to keep them warm. Serve with maple syrup, fresh berries, and a sprinkling of powdered sugar, if desired.