Heat olive oil and butter in a large skillet over medium heat.
Add sliced onions and stir to coat them in the oil and butter.
Cook the onions for about 10 minutes, stirring occasionally, until they start to soften.
Add brown sugar, salt, and pepper, and continue to cook for another 20-30 minutes, stirring frequently, until the onions are golden brown and caramelized.
If desired, stir in balsamic vinegar for added flavor and cook for an additional 2 minutes.
Remove from heat and serve warm or store for later use.
Notes
For best results, use a heavy-bottomed skillet to prevent burning.
Caramelized onions can be stored in the refrigerator for up to a week.
These onions are great on burgers, pizzas, or as a topping for steaks.