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1
In a medium bowl, combine 1 cup of the oil, the parsley, savory, the chopped fresh thyme or 4 teaspoons dried, the rosemary, the lavender flowers, if using, and the pepper.
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2
Trim off the fat from the edge of the steaks.
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3
Put the steaks in a glass dish or stainless-steel pan and rub them on both sides with the marinade.
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4
Cover and marinate in the refrigerator overnight.
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5
In a food processor, puree the butter with the olives, anchovies and 1/4 teaspoon of the salt.
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6
Cover and chill.
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7
Remove from the refrigerator 1 hour before serving.
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8
Squeeze the juice from the lemon and add it, along with the lemon halves, to a large bowl filled with cold water.
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9
Working with one artichoke at a time, remove and discard the tough outer leaves, leaving the pale-green inner ones attached.
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10
Using a small knife, trim around the bottom of the artichoke below the leaves to get rid of the remaining bits of the removed leaves.
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11
Peel the stem, leaving it about 1 inch long.
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12
Cut off the top third of the leaves.
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13
Cut the artichokes lengthwise into 1/4-inch slices and put them in the lemon water to prevent darkening.
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14
Repeat with the remaining artichokes.
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15
In a large frying pan, heat 1/3 cup of the oil over moderate heat.
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16
Add the garlic, the thyme sprigs or the remaining 1 teaspoon dried thyme, and the bay leaves and cook, stirring, for 30 seconds.
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17
Add the potatoes, 2 teaspoons of the salt, the wine and water.
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18
Cover, reduce the heat to moderately low and simmer until the potatoes are just tender, about 10 minutes.
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19
Drain the artichokes thoroughly and add them, with the remaining 1/3 cup oil, to the potatoes.
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20
Cover, bring back to a simmer and cook, stirring occasionally, until the artichokes are tender, about 10 minutes longer.
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21
If all the liquid evaporates, add up to 1/4 cup water during cooking.
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22
Set aside, covered.
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23
Light the grill or heat the broiler.
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24
Sprinkle the steaks with the remaining 1/2 teaspoon salt.
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25
Grill or broil the steaks for 6 minutes.
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26
Turn them and cook to your taste, about 6 minutes longer for medium rare.
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27
Transfer the steaks to a carving board and leave to rest in a warm spot for about 5 minutes.
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28
Reheat the potatoes and artichokes while the steaks rest.
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29
Cut the steaks into thin slices.
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30
To serve, put a mound of the potatoes and artichokes in the center of each plate.
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31
Arrange the steak slices, overlapping, on the vegetables and top with a spoonful of the room-temperature olive butter.