Melt the butter in a cast-iron skillet over medium heat. Add the green onions, red onion, Vidalia onion, white onion and brown sugar and saute for 10 to 15 minutes, stirring occasionally. Add the vinegar and Worcestershire and continue cooking until the onions are very soft and a caramel color, another 4 to 5 minutes. Stir in the cream cheese until it is melted into the onions. Remove the mixture to a large bowl, then stir in the sour cream, mayonnaise and chives. Transfer to an 8-inch square baking dish and top with the Parmesan. Bake until golden and bubbling, 15 to 20 minutes. Serve with crostini or crudites.