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1
Heat 2 tablespoons of the olive oil over medium heat in a large, heavy saucepan, and add the onion.
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2
Cook, stirring, until tender, five to six minutes.
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3
Add the split peas and enough water to cover by an inch, and bring to a boil.
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4
Skim foam off the top, reduce the heat, cover and simmer one hour.
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5
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.
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6
Stir often to prevent them from sticking.
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7
The water should cloud, and some of the split peas will be intact while others will disintegrate.
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8
Continue to simmer until they have mostly disintegrated.
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9
When the beans have fallen apart and are soft and fragrant, remove the pot from the heat and cover with a clean kitchen towel.
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10
Replace the lid and let sit for 20 minutes.
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11
If the mixture looks more like a soup than a puree, with most of the liquid on the top, place a strainer over a bowl and pour the mixture into the strainer.
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12
Let sit for 10 minutes while the liquid runs through the strainer, then return the split peas to the pot.
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13
Taste and adjust salt.
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14
Moisten as desired with the broth.
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15
Add a generous amount of pepper, and whisk in the remaining olive oil and the lemon juice.
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16
Whisking helps break down the split peas and contributes to a smooth texture.
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17
Transfer to a bowl or plate, top with a drizzle of olive oil and serve.