Rinse the split peas thoroughly in cold water.
Peel the onion and cut into quarters.
Peel the carrot and slice it.
Add split peas, onion, carrot, bay leaf, and vegetable broth to a pot.
Bring to a boil and remove any foam that forms on the surface.
Reduce the heat and simmer for about 40–45 minutes, until peas and vegetables are tender and nearly creamy.
Remove the bay leaf and blend the mixture with an immersion blender until smooth. Add more broth or water if needed to adjust consistency.
Stir in olive oil, lemon juice, salt, and pepper.
Serving
Top the fava with a drizzle of olive oil, a sprinkle of chopped red onion, and a few drops of lemon juice. Serve with fresh bread. Fava can be served warm, at room temperature, or cold, and is well-suited as a dip, appetizer, or part of a mezze spread.