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1
Place the pine nuts in the bowl of a food processor fitted with a blade attachment and process until finely ground, about 20 seconds.
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2
Scrape down the sides of the bowl using a rubber spatula.
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3
Add the measured salt and pepper, garlic, basil, and parsley; process until pureed, about 15 seconds; and scrape down the sides of the bowl.
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4
With the processor running, slowly add the oil in a thin stream until incorporated.
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5
Add the Parmesan and pulse a few times to incorporate.
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6
Taste and season with additional salt and pepper as needed; set aside.
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7
Bring a large pot of heavily salted water to a boil over high heat.
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8
Squeeze the juice from the lemon half into a medium, nonreactive bowl and fill the bowl halfway with cold water; set aside.
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9
Working with 1 artichoke at a time, cut off the leafy top third with a serrated knife.
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10
Pull off the dark outer leaves one by one to reveal the tender yellow inner leaves.
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11
Trim the stem bottom.
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12
Cut around the outside of the artichoke with a paring knife to remove the remaining tough leaf base.
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13
Using a vegetable peeler, shave the dark green skin from the stem, smoothing the edges where the leaves were attached.
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14
Cut the artichoke in half lengthwise through the leaves and stem.
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15
Using a small spoon, gently scoop out the tough purple choke and the fuzz found between the leaves and stem; discard.
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16
Cut each artichoke half lengthwise in half again and place in the reserved lemon water.
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17
Repeat with the remaining artichokes.
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18
Prepare an ice water bath by filling a large bowl halfway with ice and water; set aside.
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19
Remove the artichoke quarters from the lemon water, drop them into the boiling salted water, and cook until just tender, about 3 to 4 minutes.
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20
Using a slotted spoon or spider, transfer the artichokes to the prepared ice water bath to cool.
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21
Keep the pot of water at a boil for the asparagus.
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22
Transfer the artichokes from the water bath to a cutting board and pat dry between towels (the drier the better).
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23
Set the artichokes aside; reserve the ice water bath.
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24
Add the asparagus to the boiling water and blanch until crisp-tender, about 30 seconds.
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25
Using a spider or tongs, transfer the asparagus to the reserved ice water bath to cool.
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26
Keep the pot of water at a boil for the pasta.
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27
Transfer the asparagus from the water bath to a cutting board and pat dry between towels.
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28
Using a vegetable peeler, shave each asparagus spear lengthwise into thin strips, then cut the strips in half crosswise.
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29
(If you have trouble peeling the last portion of the asparagus, prop the spear on the flat handle of a spatula or spoon for better leverage and continue peeling.)
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30
Place the asparagus strips in a medium bowl, along with the tops of the spears; set aside.
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31
Heat the oil in a large frying pan over medium-high heat until shimmering.
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32
Add the artichokes and sear on all sides, about 5 minutes total.
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33
Transfer to a paper-towel-lined plate and season with salt and pepper.
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34
Remove the pan from heat, pour off and discard the excess oil, and set the pan aside.
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35
Add the pasta to the boiling water and cook until al dente, about 7 minutes.
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36
Reserve 1 1/2 cups of the pasta water, then drain the pasta.
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37
Immediately return the frying pan to medium-high heat; add the reserved pesto, 3/4 cup of the reserved pasta cooking water, and the asparagus strips; stir to combine; and quickly bring to a simmer.
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38
Add the cooked pasta and toss to combine, cooking to reduce the liquid or adding more reserved pasta water as needed to reach the desired sauce consistency.
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39
Taste and season with additional salt and pepper as needed.
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40
Immediately divide among 4 warm bowls and top each bowl with 4 artichoke quarters and some pepper.
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41
Serve with grated Parmesan.
