Place the split peas in a bowl and pour tap water. Wait 2-3 minutes and use a colander to rinse them with plenty of water. Repeat until the water is crystal clear (2-3 more times). Drain and transfer to a pot.
In a pot over high heat, add 4 cups out of 6 (800ml out of 1.200ml) of water or vegetable broth, shredded carrot, sliced onion, oil olive, and bay leaves. Bring to a boil for 5 minutes. Turn the heat down to medium and simmer. Remove with a spoon the white foam that usually surfaces. It takes more or less half an hour for the initial amount of liquid to be absorbed. Add salt, pepper and cumin.
Add gradually more HOT water or broth, turn down the heat to low and stir frequently until split peas are very tender and the texture is similar to a thick soup. At that point, stir quite often. It takes more or less 50 minutes but cooking time depends on the product.
Remove from heat and add lemon. Put the mixture in a food processor or a hand blender and mix until the peas are smooth and creamy, like a puree. Add more hot water if it is too thick.
Serve with extra virgin olive oil, diced onion, thyme, freshly ground pepper.