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1
Fill a large bowl with cold water, and squeeze the juice of 3 lemon halves into the water; add the rinds.
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2
Working with 1 artichoke at a time, remove the tough outer leaves (reserve about 8 cups leaves, and discard remaining).
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3
Trim the tops so the artichokes are 1 inch long.
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4
Peel the stems to remove tough, dark-green parts, and cut the stems flat so that the artichokes can stand upright.
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5
Rub the artichokes with juice from the remaining lemon half; place the artichokes in the lemon water.
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6
Cover with damp paper towels.
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7
The artichokes can be refrigerated in lemon water overnight; cook just before serving.
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8
Put the reserved artichoke leaves and the stock into a large stockpot.
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9
Bring to a boil over medium-high heat.
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10
Reduce heat to medium-low, and simmer for 10 minutes.
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11
Pour through a fine sieve into a large bowl, and discard the leaves (you should have about 4 cups liquid).
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12
Set aside.
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13
Melt the butter in a medium stockpot over medium-high heat.
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14
Add the onions, 1/2 teaspoon salt, and 1/4 teaspoon pepper.
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15
Cook, stirring occasionally, until the onions are translucent, about 4 minutes.
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16
Add the potatoes and reserved artichoke broth.
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17
Bring to a boil over medium-high heat.
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18
Reduce heat to medium-low.
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19
Simmer, partially covered, until the potatoes are tender when pierced with the tip of a knife, 10 to 15 minutes.
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20
Let cool slightly.
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21
Meanwhile, fill a clean large stockpot with 2 inches of water.
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22
Insert a steamer basket, and bring water to a boil.
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23
Add the artichoke hearts to steamer basket.
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24
Cover, and steam until artichoke hearts are tender but not falling apart, 15 to 20 minutes (begin checking after 15 minutes).
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25
Season with salt.
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26
Transfer the artichoke hearts to a platter, and cover to keep warm.
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27
Working in batches, coarsely puree the soup in a food processor (do not overprocess).
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28
Pass through a medium-mesh sieve into another pot.
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29
Season with salt and pepper.
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30
The soup can be refrigerated in an airtight container overnight; reheat over medium-low heat before serving.
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31
Ladle the soup into bowls.
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32
Fan leaves of artichoke hearts, if desired; place 3 hearts in each bowl.
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33
Garnish soup with chives.