PREPARE the artichokes: Fill a small bowl with cool water and the juice of 1 lemon. Start by snapping off all of the outer leaves until you’re just left with the inner yellow leaves. Trim the nubs left behind by the outer leaves with a paring knife. Trim off the bottom inch of the stem and peel off the exterior of the stem to reveal the yellow interior. Trim the remaining leaves off with a sharp knife so that they are flush with the base of the artichoke. Drop the trimmed artichoke in the lemon water and repeat with the other artichoke.
PLACE both prepared artichokes and their lemon water in your Instant Pot. Add enough water, if needed, so that the artichokes barely float. Add the juice of 1 lemon. Secure the lid.
COOK at high pressure for 10 minutes and use a quick release.
MEANWHILE, cook the linguine in salted water according to the package directions and drain.
ONCE the pressure has released, remove the artichokes and let them cool a bit. Clean the pot. Once the artichokes are cool enough to handle, remove any remaining leaves to expose the choke. Scoop all of the feathery and tough bits out and discard. Chop the remaining tender hearts.
TURN on the Saute function. Once hot, add the oil followed by the garlic. Saute for 30 seconds and add peas and broth. Simmer for 2 minutes and turn off the Saute function. Add the artichokes, parmesan, zest, and juice of 1 lemon, parsley, and pepper flakes. Season with salt and pepper.
ADD the pasta and toss. Serve topped with more parmesan.