Cut the pork shoulder into 4 to 6 similar-sized pieces and season generously with salt and pepper.
Set the Instant Pot to Sauté. Add a tablespoon of oil, and once hot, add two or three pieces of pork, working in batches so you don’t crowd the pot. Sear each side for 2 to 3 minutes or until deeply golden, then transfer to a plate and repeat with the rest.
Add a bit more oil if the pot’s looking dry. Add the onions, carrots, and celery, and season with a pinch of salt. Sauté until softened and the onions turn translucent.
Stir in the garlic and let it cook for just 30 seconds—just until fragrant.
Stir in the tomato paste, coating the vegetables, then pour in the wine. As it simmers, scrape up any browned bits stuck to the bottom of the pot—this is all flavor! Let it bubble away for 3 to 4 minutes until the liquid has reduced.
Add the porcini mushrooms, bay leaves, herbs, crushed tomatoes, broth, and a pinch of salt and pepper. Nestle the pork chunks back into the pot, then add the parmesan rind.
Lock the lid, set the valve to seal, and cook on manual high pressure for 40 minutes. Let the pressure release naturally for 15 minutes, then finish with a quick manual release.
Transfer the pork to a cutting board and let it rest for about 10 minutes.
While the pork rests, switch the Instant Pot back to Sauté and let the sauce simmer gently for about 5 minutes, or until it’s reduced and thickened slightly.
To temper the cream, add the cream to a small mixing bowl. Slowly ladle in about a cup of the hot tomato sauce, whisking constantly as you go. This will gently warm the cream so it won’t curdle when it hits the pot.
Turn the Instant Pot off, and stir the tempered cream into the tomato sauce.
Once the pork has rested, use two forks to shred it—it should just fall apart. Discard any big pieces of fat as you go. When done, stir the shredded pork into the sauce.
Serve over pappardelle noodles or mashed potatoes.