1. Heat 2 tablespoons of the olive oil over medium heat in a large, heavy saucepan, and add the onion. Cook, stirring, until tender, five to six minutes. Add the split peas and enough water to cover by an inch, and bring to a boil. Skim foam off the top, reduce the heat, cover and simmer one hour. Add salt to taste, and continue to simmer for 30 minutes to an hour until the beans fall apart and sink to the bottom of the pot. Stir often to prevent them from sticking. The water should cloud, and some of the split peas will be intact while others will disintegrate. Continue to simmer until they have mostly disintegrated.

2. When the beans have fallen apart and are soft and fragrant, remove the pot from the heat and cover with a clean kitchen towel. Replace the lid and let sit for 20 minutes. If the mixture looks more like a soup than a purée, with most of the liquid on the top, place a strainer over a bowl and pour the mixture into the strainer. Let sit for 10 minutes while the liquid runs through the strainer, then return the split peas to the pot. Taste and adjust salt. Moisten as desired with the broth. Add a generous amount of pepper, and whisk in the remaining olive oil and the lemon juice. Whisking helps break down the split peas and contributes to a smooth texture. Transfer to a bowl or plate, top with a drizzle of olive oil and serve with pita bread, endive or small romaine lettuce leaves, or crudités for dipping.

Yield: Serves six to eight.

Advance preparation: This will keep for three or four days in the refrigerator. Retain any liquid that you’ve poured off from the pot, as the peas will continue to thicken and stiffen and you will probably want to thin them out. Reheat gently and serve.