In a large pan, add olive oil, vegetal butter, some salt and the onions, stir and cook on medium heat

When the onions start the brown, lower the the heat and cook for about 10 minutes

Then add the vinegar, mustard, lemon juice, salt and pepper (to taste) and parsley and stir with the onions. Let it cook on low heat for 3 minutes.

Add the water, olive oil, and green olive and cook for 5 more minutes. The onions should be soft, sweet and a little acid, and the sauce should be tasty.