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1
In a medium bowl, whisk the flour and lemon juice together to make a paste, then whisk in 6 cups cold water.
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2
One at a time, cut away the stems of the artichokes and rub each bottom with a lemon half Remove and discard the tough outer leaves until those exposed are folded inward and are creamy green in color.
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3
Cut off the cone of leaves halfway down from the top and discard.
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4
Rub the cut surface with the used lemon half and drop into the water-flour mixture.
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5
Fill a large nonreactive pot with lightly salted water and bring to a boil.
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6
Squeeze the remaining lemon half into the boiling water.
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7
Add the drained artichokes, reduce the heat, and simmer about 30 minutes until the bottoms are tender and can be easily pierced with a sharp paring knife.
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8
Remove the artichoke bottoms with a slotted spoon to a colander, cool under cold running water, and drain.
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9
(The hearts can be prepared one day ahead: prepare up to this point, cover, and refrigerate.)
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10
Carefully remove the remaining leaves, disturbing the bottom as little as possible.
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11
Scrape out the choke with the tip of a spoon.
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12
Trim the sides to make a neat shape.
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13
Shave the bottoms flat so they will sit level.
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14
Cover and keep warm, or reheat in a steamer over boiling water.
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15
In a medium saucepan of lightly salted boiling water, cook the carrots until tender, about 6 to 8 minutes.
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16
Drain, and puree in a food processor.
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17
Season with salt and pepper and keep warm in a double boiler over simmering water.
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18
Prepare the beurre blanc: In a nonreactive medium saucepan, boil the orange juice and white wine over medium heat until the liquid is syrupy and reduced by two-thirds, about 12 minutes.
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19
Remove the pan from the heat and whisk in 2 tablespoons of the butter, one piece at a time.
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20
Return to low heat and, whisking constantly, add the remaining butter, one piece at a time.
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21
When all of the butter is added, the sauce will have the creamy smooth consistency of a hollandaise.
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22
Remove the pan to the warm side of the stove to keep warm.
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23
Bring a large saucepan of water to a simmer.
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24
Add the vinegar.
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25
One at a time, carefully break each egg into the water.
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26
Using a large spoon, quickly life the setting white around each egg and spoon it towards the egg yolk to help the eggs poach into oval shapes.
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27
Simmer gently until the whites are firm, but the yolks are still soft, about 4 minutes.
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28
Use a slotted spoon to transfer the eggs to paper toweling to drain briefly.
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29
Trim away some of the whites so the eggs will sit neatly on top of the artichoke hearts.
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30
Set the cooked poached eggs aside in a bowl of ice water until ready to serve, up to 2 hours.
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31
(You should have extra eggs on hand just in case any should break.)
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32
Bring a skillet of plain water to a simmer.
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33
With a slotted spoon, transfer the poached eggs to the water and heat through, about 2 minutes.
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34
Place the artichoke hearts on individual warm plates and fill the wells with a spoonful of the carrot puree.
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35
Use the slotted spoon to place the eggs on top of the puree.
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36
Spoon the beurre blanc over the eggs and sprinkle with chives.
