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1
Fill a large bowl with water.
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2
Cut 2 of the lemons in half, squeeze the lemon into the water, and drop the lemon halves into the water.
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3
Remove the outer leaves from the artichokes until you are left with only the light green centers.
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4
Cut off and discard the tough stem ends of the artichokes, leaving as much as 1 or 2 inches of stem attached.
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5
Using a vegetable peeler or a small sharp knife, shave the artichoke stems, revealing the light green inner stems.
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6
Cut 1/2 inch to 3/4 inch off the tip ends of the artichoke leaves so they have flat tops and discard all of the trimmed leaves and bits.
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7
Place the trimmed artichokes in the lemon water as you finish them.
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8
(You can prepare the artichokes to this point up to a day in advance.
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9
Leave them in the lemon-water until youre ready to braise them.)
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10
Pour 1/4 cup of the olive oil into a large saute pan; add the onion and garlic, season with salt, and cook over high heat for about 2 minutes, until the onion just begins to soften.
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11
Add the artichokes and season with salt.
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12
Turn off the heat.
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13
Pour in enough olive oil to cover the artichokes; the amount will vary depending on the size of the pan youre cooking them in.
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14
Squeeze the remaining lemon into the pan with the artichokes and drop the squeezed halves into the olive oil.
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15
Add the rosemary sprigs.
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16
Place a large paper coffee filter or a piece of cheesecloth on top of the artichokes and pat it down to saturate the paper or cloth with the oil so that it rests directly on the surface of the oil to help keep the artichokes submerged.
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17
Turn the heat on high to heat the oil until it begins to boil just around the edges of the pot; you dont want the oil at a rolling boil.
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18
Reduce the heat to low and cook the artichokes without tending them for 25 to 35 minutes, until they are just barely tender when pierced with a small, sharp knife; they will continue gently cooking as they sit in the oil, making them very tender and buttery.
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19
Remove the pot from the heat, remove and discard the coffee filter or cheesecloth, and let the artichokes cool in the oil to room temperature.
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20
Drain the artichokes in a colander, reserving the oil.
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21
Remove and discard the onion, garlic, and lemon.
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22
Store the artichokes in the oil and transfer them to an airtight container and refrigerate for up to one week.
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23
Bring the artichokes to room temperature and drain before using them.
