In a large pot over medium heat, warm 1 cup of olive oil and cook the onions and carrots until they soften about 7-8 minutes. Mix the garlic and mix to cover the olive oil.
Add the yellow divided peas and also mix to cover the oil. Add enough water or stock to cover the content of the pot of about 2 inches. Add the bay leaves.
Bring over low heat over medium heat, reduce and cook uncovered, until the liquid is almost absorbed, about 45 minutes. As you cook, it may be necessary to add a liquid in an incremental way while the split peas cook until they are soft and disintegrated in a flour puree.
The final plot should appear like this: there should not be a subtle liquid left on the surface; It should break out in fat, not in bubbles; And when drawing a wooden spoon through the Fava, it should take a clear path on the bottom of the pot. Remove it from the fire and place a towel on the bean to let it cool and thicken by allowing the steam to escape.