This pasta dish is springtime on a plate. Fat asparagus spears are peeled lengthwise into thin ribbons that twist nicely around the fettuccine. Toss the asparagus-fettuccine mixture in a basil-parsley pesto, then top it with seared baby artichokes.
Place the pine nuts in the bowl of a food processor fitted with a blade attachment and process until finely ground, about 20 seconds. Scrape down the sides of the bowl using a rubber spatula. Add the measured salt and pepper, garlic, basil, and parsley; process until puréed, about 15 seconds; and scrape down the sides of the bowl.
With the processor running, slowly add the oil in a thin stream until incorporated. Add the Parmesan and pulse a few times to incorporate. Taste and season with additional salt and pepper as needed; set aside.
For the pasta:
Bring a large pot of heavily salted water to a boil over high heat.
Squeeze the juice from the lemon half into a medium, nonreactive bowl and fill the bowl halfway with cold water; set aside.
Working with 1 artichoke at a time, cut off the leafy top third with a serrated knife. Pull off the dark outer leaves one by one to reveal the tender yellow inner leaves. Trim the stem bottom. Cut around the outside of the artichoke with a paring knife to remove the remaining tough leaf base. Using a vegetable peeler, shave the dark green skin from the stem, smoothing the edges where the leaves were attached. Cut the artichoke in half lengthwise through the leaves and stem. Using a small spoon, gently scoop out the tough purple choke and the fuzz found between the leaves and stem; discard. Cut each artichoke half lengthwise in half again and place in the reserved lemon water. Repeat with the remaining artichokes.
Prepare an ice water bath by filling a large bowl halfway with ice and water; set aside.
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. Using a slotted spoon or spider, transfer the artichokes to the prepared ice water bath to cool. Keep the pot of water at a boil for the asparagus. Transfer the artichokes from the water bath to a cutting board and pat dry between towels (the drier the better). Set the artichokes aside; reserve the ice water bath.
Add the asparagus to the boiling water and blanch until crisp-tender, about 30 seconds. Using a spider or tongs, transfer the asparagus to the reserved ice water bath to cool. Keep the pot of water at a boil for the pasta. Transfer the asparagus from the water bath to a cutting board and pat dry between towels. Using a vegetable peeler, shave each asparagus spear lengthwise into thin strips, then cut the strips in half crosswise. (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.) Place the asparagus strips in a medium bowl, along with the tops of the spears; set aside.
Heat the oil in a large frying pan over medium-high heat until shimmering. Add the artichokes and sear on all sides, about 5 minutes total. Transfer to a paper-towel-lined plate and season with salt and pepper. Remove the pan from heat, pour off and discard the excess oil, and set the pan aside.
Add the pasta to the boiling water and cook until al dente, about 7 minutes. Reserve 1 1/2 cups of the pasta water, then drain the pasta.
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. 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. Taste and season with additional salt and pepper as needed.
Immediately divide among 4 warm bowls and top each bowl with 4 artichoke quarters and some pepper. Serve with grated Parmesan.