In a small pot, combine fava beans, water or vegetable stock, onion, carrot, bay leaf, and coarse sea salt. Stir gently and bring to a boil over medium-high heat.

Once boiling, reduce heat to low, cover, and simmer for 40 to 50 minutes without stirring, until beans are tender and creamy.

Carefully uncover and remove carrot, onion, and bay leaf. Discard them for smooth texture.

Mash fava beans to desired consistency using a spoon or immersion blender.

Stir in olive oil and lemon juice, mixing well and adjusting thickness with water if needed.

Transfer to a serving bowl and garnish with capers, red onions, and diced tomatoes. Drizzle with additional olive oil.

Serve warm or at room temperature with lemon halves on the side.