Add the onions to a heavy bottom pot with the butter. Season with salt and pepper. Cook on medium high, stirring often, to brown, about 25 minutes. The onions will drastically reduce in size.
Add the beef and cook 5 minutes to brown and break up.
Add the cumin and chipotle with the sauce. Cook 3 minutes stirring and breaking up the pepper.
Add the oregano, stock, vinegar, and water. Stir well to combine. Bring to a simmer and cook 30 minutes.
Preheat oven to 450.
Build quesadillas with one tortilla on the bottom, about 1/2 cup cheese in the center, and one tortilla on top.
Cook the quesadillas in a hot pan with some butter to brown on both sides and melt the cheese.
Ladle the soup into 4 oven safe bowls. Top each with a quesadilla, pressing it down to soak up some of the soup, and then flipping it so that it is wet on the top. This will help it soften throughout.
Split the remaining cheese amongst the 4 bowls on top of the quesadilla. Place the bowls on a baking sheet and bake for 20 minutes to melt the cheese and slightly brown the top.
Allow to cool for 5 minutes before serving.