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1
Trim the hard green parts from the leeks; split in half from about an inch below the root end (leave this intact for now) to the leafy end.
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2
Carefully wash between all the layers, removing all traces of sand.
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3
Cut off the root end and cut the leeks into 4-inch sections.
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4
Put all but a tablespoon of the oil in a skillet with a lid or a saucepan large enough to hold the leeks in one layer.
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5
Turn the heat to medium.
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6
When the oil is hot, add the leeks and carrots, along with a sprinkling of salt and pepper, and cook for about 25 minutes, turning occasionally, until the leeks are tender.
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7
Your goal is not to brown the leeks but to soften them; if they brown a little, however, thats fine.
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8
Add the rice and 1 1/2 cups of water, cover, and adjust the heat so the mixture simmers.
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9
Cook for about 30 minutes, or until the water is absorbed; the mixture should be moist but not soupy.
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10
Serve hot, at room temperature, or cold (this will keep well, covered and refrigerated, for a day, and can be reheated).
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11
Just before serving, drizzle with the remaining olive oil and the lemon juice.
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12
In step 2, omit the carrots.
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13
In step 3, omit the rice and add 1/2 cup pitted black olives, like Kalamatas.
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14
Use only 1/2 cup liquid and cook for only 5 to 10 minutes, until hot.
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15
Add the lemon juice at the end.
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16
You can use this formula with almost any braised vegetable: When the leeks are done, beat 2 eggs in a bowl with the minced or grated zest and juice of a lemon; still beating, add about 1/2 cup of the leek-cooking liquid.
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17
Gradually add the remaining cooking liquid, beating all the while.
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18
Dress the leeks with this sauce and serve.
