Melt butter in a large pot over medium-high heat. Stir in salt, red onions and sweet onions. Cook 35 minutes, stirring often, until onions are caramelized.
Mix in the chicken and beef broths, red wine and Worcestershire sauce. Bundle the parsley, thyme, and bay leaf with twine and place in pot. Simmer over medium heat for 25 minutes, stirring occasionally. Remove and discard the herbs. Reduce heat to low and add the vinegar. Season with salt and pepper, them cover and simmer over low.
Arrange bread slices on a baking sheet and broil on each side until well toasted. Remove from heat; do not turn off broiler.
Arrange 4 large oven safe bowls or crocks is a baking pan or sheet with rims. Fill each bowl 2/3 full with hot soup. Top each bowl with 1 slice of bread and sprinkle cheeses, to taste, on the bread.
Broil 5 minutes, or until bubbly and golden brown. As the cheese softens it will spill over the bowl and create a delicious cheese bubble.