Heat a large sauté pan, or skillet, over medium low heat. Add 1 tablespoon of butter and, once it melts, add the sliced onions and stir them gently to coat with butter. Cook for about 10 minutes, stirring often, or until they are soft and start to get golden brown. Add the balsamic vinegar and scrape any browned bits from the bottom of the pan. Continue cooking for an extra 5 to 10 minutes, or until they are caramelized and golden brown! Season with salt and pepper and reserve.
In that same pan, over medium heat, heat the olive oil and cook the sausage, breaking it apart with a wooden spoon, until it is no longer pink. Then, add the kale leaves and continue cooking until the sausage is cooked through and the kale has softened. Season with salt and pepper and reserve.
To assemble the grilled cheese sandwiches, spread the remaining butter evenly on all bread sides.
Layer each bottom with cheese, sausage and kale mixture, caramelized onions and finish with some more cheese. Top each sandwich with its top bread slice and place them in a sauté pan, over medium heat. Grill for 2 to 3 minutes or until the bread is golden brown. Flip and cook on the other side for 2 more minutes or until golden brown and the cheese has melted.
Slice and serve immediately!