8 cups yellow onions, thinly and uniformly sliced (see note)
Salt and pepper, to taste
1 tbsp. balsamic vinegar
2-½ cups Gruyère, shredded
4 small brioche buns, cut in half crosswise
Instructions
In a Dutch oven or large, heavy skillet, over medium heat, heat the olive oil and 1 tablespoon butter.
Once the butter melts, add the sliced onions and a large pinch of salt; if the onions are particularly large, another tablespoon of butter may be needed to thoroughly moisten.
Cook, stirring occasionally, until the onions are softened and translucent; 7 to 10 minutes.
Reduce the heat to medium-low and continue cooking, stirring occasionally, until the onions are deep brown all over; 1 hour to 1-¼ hours total, reducing the heat to low if they are browning unevenly.
If the onions start to stick to the bottom of the pan and/or burn, reduce the heat to low and add the balsamic vinegar, stirring to deglaze the browned bits from the bottom of the pan.
When the onions are caramelized, stir in the balsamic vinegar if you haven’t already added it; remove from heat.
Heat the oven to broiler on low.
Place the halved brioche buns, opened, on a sheet pan.
Divide the cheese evenly among each bun half and broil until melted; 3 to 4 minutes.
Remove the buns from the oven and sprinkle with ground black pepper.
Add 2 tablespoons or caramelized onions to the bottom half of each bun.
Complete the sandwich by placing the two halves together and serve.
Notes
Onions that are sliced uniformly will brown more evenly; onions that are sliced thinly will caramelize faster.