Peel and finely chop the onions. Put peas in a large pot and add enough water (approx. 600 ml) to cover the peas. Bring to the boil and simmer for about 5 minutes until steam is rising.
Pour off the water and add again so much water that the peas are covered.
Add half onion cubes and about 1/2 tsp. salt, place the pot back on the stove. Simmer the peas for 30-40 minutes until they are soft and crumble easily. Stir several times so that the peas do not burn.
Meanwhile peel, wash and chop the potatoes. Add to the peas about 15 minutes before the end of the cooking time.
Wash parsley, shake dry, pluck off leaves and chop finely. Squeeze lemon. Stir the juice into the peas. Stir the peas vigorously several times with a wooden spoon. Season with salt and pepper.
Sprinkle parsley and onions over the puree. Finally sprinkle Fáva with olive oil and serve.