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In a large pot, heat olive oil over medium heat and sauté the onion until softened, about 8 – 10 minutes. Rinse the split peas in a sieve and add to the onion, stirring well to coat in the oil. Pour water or broth, or a combination of the two.
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Bring to boil over high heat, reduce heat. Reduce heat and add the bay leaves, thyme, salt and pepper. Simmer until tender, about 50 minutes to 1 hour. Skim the foam off the surface as the soup simmers.
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Transfer the soup to the bowl of a food processor, or, using an immersion blender, process the soup to a smooth puree. Test for salt and pepper and add if needed. Stir in lemon juice. Dilute the soup if necessary with additional water or stock, making sure to reheat as you stir.
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To serve, ladle the soup into serving bowls and garnish with a few drops of truffle oil, pink peppercorns and a few pieces of cured pork.