01 -
Heat 2 tablespoons of butter in a big skillet over medium-high heat. Toss in onions with some salt and pepper, then cover and let them soften for about 3 to 5 minutes, stirring now and then. Take the lid off, lower the heat to medium-low, and cook until they've turned deep gold—around 20 to 25 minutes. If they stick to the pan or dry out, add small splashes of water and scrape up the brown bits. Want more flavor? Deglaze with vinegar and cook it off, stirring for about a minute. Scoop these into a bowl, season more if needed, and set aside. Clean the pan if needed.
02 -
Stir the grated cheese into the onions to combine. Lay two slices of bread flat, spread the onion-cheese mix on them evenly, then cover with the remaining bread. Press gently so the layers stick together.
03 -
Melt 1 tablespoon of butter in the same pan over medium heat. Place the sandwiches in and cook for 3 to 4 minutes until the bottom is toasted and golden. If it browns too quickly, lower the heat. Add the last tablespoon of butter, flip sandwiches, press lightly, and cook until the cheese is gooey and the other side is just as crispy, another 3 to 4 minutes. Serve while warm.