Place a deep pot over medium to high heat, pour a little olive oil, the carrot and mix with a wooden spoon.
Add the onion, stir and sauté until the vegetables caramelize.
After about 3 minutes, add the split peas, the smoked paprika, stir again and sauté for another 2 minutes.
Add the hot water, the vegetable bouillon cube, the bay leaves, stir and simmer over medium heat for about 20 minutes, until the split peas soften.
When soft, remove from heat, remove the bay leaves, pour the olive oil, apple cider vinegar, add a little salt and pepper and mash the fava puree with the hand blender or in a food processor. When ready, set aside.