Option to trim pork of excess fat. Then season pork with parsley, oregano, thyme, and a generous amount of salt and pepper.
On the Instant Pot, turn on Sauté: Normal mode and add oil. When it reads "Hot", add half the pork shoulder, making sure not to overcrowd the pot. Sear each side for 2-3 minutes until deeply browned, then transfer to a plate. Repeat with second half and set aside.
Add onion, carrots, and celery. Sauté for 3-4 minutes or until edges of onion starts to get translucent. Add garlic and cook for additional 30 seconds.
Pour in the wine. Scrape up browned bits on the bottom of the pot and reduce for 4-5 minutes. Then turn off Sauté mode.
Add bay leaf and tomato sauce. Pour broth into tomato can to get all the sauce, and add into Instant Pot along with a pinch of salt and pepper. Nestle in pork. Place the lid on and seal. Cook on Manual Pressure: High for 30 minutes, then let release naturally for 10 minutes.
Remove the pork and shred. Meanwhile, turn Sauté mode on the Instant Pot and let boil for 5-10 minutes or until sauce has reduced to preferred thickness.
Stir shredded pork back into the sauce. Remove the bay leaf, season sauce to taste, and serve. Garnish with grated Parmesan cheese and fresh basil.