In a 5 to 6 quart thick-bottomed pot, heat 3 tablespoons of olive oil on medium heat. Add the onions and toss to coat with the olive oil. Cook the onions, stirring often, until they have softened, about 15 to 20 minutes.
Increase the heat to medium high. Add the remaining tablespoon of olive oil and the butter and cook, stirring often, until the onions start to brown, about 15 more minutes.
Then sprinkle with sugar (to help with the caramelisation) and 1 teaspoon of salt and continue to cook until the onions are well browned, about 10 to 15 more minutes.