Heat the butter in a large saute pan over medium heat, until melted.
Add the onions and 2 tablespoons (29.57 milliliters) of broth. Saute for 10-15 minutes, stirring occasionally but not constantly.
Add 2 more tablespoons of broth to keep the onions hydrated, and scrape the bottom to deglaze. Continue to saute for 10-20 more minutes, until browned and caramelized. (Time will vary depending on your stove, pan size and material, and size and shape of the onions. Reduce heat if they start to brown too much.)