Prepare the split peas: Place 500 g of yellow split peas (Greek fava) in a large bowl. Add 500 ml of water, stir well, and set aside while preparing the vegetables.
Prepare the vegetables: Peel and roughly slice 2 medium carrots. Roughly chop 1 medium onion.
Sauté the vegetables: Heat 30 ml of extra virgin olive oil in a pot. Add the chopped onion and carrots and sauté for 3–4 minutes, until slightly softened.
Season and add the water: Season with salt and black pepper to taste, then pour in 1 litre of water.
Rinse and drain the split peas: Thoroughly rinse and drain the soaked split peas, then add them to the pot with the vegetables.
Add the garlic and oregano: Cut 1 large garlic clove into chunks and add it to the pot, along with 1 teaspoon of dried oregano. Stir to combine.
Skim and simmer: Allow the mixture to simmer gently and skim off any foam that rises to the surface. Reduce the heat to low and simmer for approximately 30 minutes, until the split peas are completely soft and tender.
Stir towards the end: As the fava thickens, stir frequently, especially towards the end of cooking, to prevent it from sticking to the bottom of the pot and burning.
Blend until creamy: Remove the pot from the heat. Using an immersion blender or food processor, blend the mixture until completely smooth and velvety.
Add the lemon and olive oil: Squeeze in the juice of half a lemon and add 2 tablespoons of extra virgin olive oil. Stir thoroughly until fully incorporated.
Garnish and serve: Transfer the fava purée to a serving plate and top with finely chopped red onion and capers. Finish with a generous drizzle of extra virgin olive oil and serve.