Heat the oil in a large skillet over medium heat. Saute the onions until soft and caramelized, about 25 minutes. Season with salt and pepper. Transfer the onions to a plate.
Generously butter both sides of each bread slice. In between two bread slices, pile the caramelized onions between two layers of cheese.
Heat a large skillet or griddle over medium-low heat. Cook the sandwiches, flipping once, until the cheese is melted and the bread is golden brown, 2 to 3 minutes per side.
Serve with Creamy Tomato Soup.
Heat the oil in a large saucepan over medium heat. Add the garlic and onions and cook until the onions are translucent, about 5 minutes. Add the brown sugar and tomatoes and cook for 5 minutes more. Add 1/2 cup water, the thyme and Parmesan rind, if using. Cook for about 25 minutes.
Discard the thyme sprigs and Parmesan rind. Puree the soup in a food processor or with an immersion blender until smooth. Strain through a fine sieve set over cleaned saucepan. Stir in the cream and butter. Season with salt and pepper.
To serve, ladle the soup into bowls and sprinkle with Parmesan and chives.