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1
Trim the artichokes: Remove all the tough outer leaves and then, with a very sharp knife, cut off the top of the choke (about an inch) to remove the sharp tips. If you are lucky enough to have a artichoke with stalk, peel the stalk with a vegetable peeler.
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2
Cut the choke in half lengthwise. With a spoon, scoop out the hairy choke, but be careful not to remove the heart. Put the chokes in a bowl with some lemon juice so they do not turn brown.
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3
Heat your grill to high. In a pot of water, squeeze half of the lemon. Add the chokes and simmer for about 15 minutes until they are tender. You can also steam them, if you prefer. Remove the chokes from the water and drain.
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4
Mix together the oil and garlic, then brush the mixture on the artichokes and place them on the hot grill.
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5
Continue to brush the chokes with the garlic-oil mixture and keep turning them so that they do not burn. After a few minutes, remove them from the grill. Sprinkle with a little sea salt.
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6
Place the tarragon leaves, garlic cloves, and salt in a clean mortar. (I always fill mine with hot water, pour it out, and dry it before using.)
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7
Begin pounding with the pestle until the ingredients start to form an emulsion. This will take several minutes.
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8
Add the egg yolks and continue to mix with the pestle.
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9
When the egg yolks are incorporated, SLOWLY start to add the olive oil a few drops at a time; this will start to emulsify.
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10
When all the olive oil has been added and you have a beautiful green mayonnaise, add the lemon juice and incorporate it into the emulsion. Then let it refrigerate and rest for a while.
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11
This is the dipping sauce for the artichokes, and it should be made ahead of time. It's also good on a lot of other vegetables (like grilled fennel).
