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1
Blanch 3/4 cup basil in a 2-quart saucepan of boiling salted water 2 minutes, then drain in a sieve and plunge into a bowl of ice water to stop cooking.
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2
Drain basil again and press out excess liquid.
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3
Puree basil with grapeseed oil in a blender 2 minutes.
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4
Pour mixture into an airtight container and chill 8 to 12 hours.
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5
Pour through a very fine sieve into a small bowl (do not press on solids).
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6
Squeeze juice from 1 lemon half into a large bowl of water, then drop same half into water.
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7
Keep stem attached and, at opposite end, cut off top inch of 1 artichoke with a serrated knife.
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8
Bend back outer leaves until they snap off close to base, then discard several more layers in same manner until you reach pale yellow leaves with pale green tips.
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9
Cut remaining leaves flush with top of artichoke bottom using a sharp knife, then trim dark green fibrous parts from base and sides of artichoke.
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10
Rub cut surfaces with remaining lemon half.
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11
Cut 1/4 inch from stem to expose inner core.
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12
Trim sides of stem (still attached) down to pale inner core.
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13
Rub cut surfaces with same lemon half.
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14
Cut artichoke into 4 wedges, then cut out any remaining purple leaves and fuzzy choke and drop artichoke wedges into lemon water.
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15
Prepare remaining 3 artichokes in same manner.
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16
Cook onion in olive oil in a 12-inch heavy skillet over moderate heat, stirring occasionally, until softened, about 5 minutes.
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17
Drain artichokes and pat dry with paper towels.
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18
Arrange artichokes over onion, then add wine and simmer, covered, until artichokes are tender, 30 to 40 minutes.
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19
Transfer mixture with a slotted spoon to a large bowl and keep warm, covered.
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20
Pat shrimp dry and sprinkle with salt, cayenne, and 1 tablespoon orange dust.
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21
Heat butter in cleaned skillet over moderately high heat until foam subsides, then cook shrimp until just cooked through, about 2 minutes on each side.
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22
Toss arugula, remaining 1/2 cup micro-basil, lemon juice, and remaining 2 teaspoons orange dust with artichoke mixture and season with salt.
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23
Divide mixture among 4 plates and arrange shrimp around salad.
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24
Drizzle each serving with some basil oil and sprinkle with additional orange dust.