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1
Cut the leeks in half lengthwise and rinse well under cold running water until clean.
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2
Tie 1 leek half and the parsley stems together with butchers twine and place in a large saucepan.
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3
Add the lentils, bay leaf, and garlic and cover the lentils with cold water by 2 inches.
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4
Cover the pan with a tightfitting lid and bring to a boil over medium-high heat, about 10 minutes.
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5
Uncover, reduce the heat to medium low, and simmer, stirring occasionally, for 15 minutes.
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6
Add 1 teaspoon of the salt, stir to combine, and continue to simmer until the lentils are just tender, about 10 to 12 minutes more.
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7
Meanwhile, finely chop the 3 remaining leek halves.
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8
Heat 2 tablespoons of the oil in a large frying pan over medium heat until shimmering.
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9
Add the chopped leeks, carrots, onions, and a pinch each of salt and pepper and cook, stirring often, until the onions are translucent and the carrots are just tender, about 4 to 5 minutes.
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10
Taste and season with more salt and pepper as needed.
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11
Transfer the mixture to a large heatproof bowl.
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12
Using tongs, remove the leek bundle, bay leaf, and garlic clove from the lentils and discard.
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13
Drain the lentils through a large fine-mesh strainer and transfer to the bowl with the carrot mixture.
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14
Add the measured vinegar, the remaining 2 tablespoons olive oil, and the remaining 1 teaspoon salt and stir to combine.
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15
Taste and season with more salt, pepper, and vinegar as needed.
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16
Stir in the chopped parsley.
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17
Serve warm or at room temperature.