Cut the pork shoulder into 1.5-inch (4 cm) cubes, trimming excess fat. Pat completely dry with paper towels, then season all sides with 1 teaspoon kosher salt and 1/2 teaspoon black pepper.
Press Sauté (high) on the Instant Pot, heat 1.5 tablespoons olive oil, then sear the pork in two batches for 3 to 4 minutes per side until golden brown. Transfer seared pork to a plate and repeat with remaining oil and pork.
Add the diced onion and celery to the pot and cook for 3 to 4 minutes until softened, then add the garlic, tomato paste, smoked paprika, thyme, and rosemary and stir for 1 to 2 minutes until fragrant.
Pour in the red wine and use a wooden spoon to scrape up all browned bits from the bottom of the pot. Let the liquid bubble and reduce for about 2 minutes, ensuring the bottom is completely clean.
Return the seared pork to the pot along with the chicken broth and Worcestershire sauce, then add the carrots and potatoes on top. Lock the lid, set the valve to Sealing, and pressure cook on high for 25 minutes.
Allow the pressure to naturally release for 10 minutes, then carefully switch the valve to Venting to release remaining steam. Open the lid only after the float valve has dropped.
Press Sauté, bring the stew to a simmer, and stir in the cornstarch slurry. Cook for 2 to 3 minutes, stirring constantly, until the broth reaches your desired consistency, then taste and adjust seasoning.
Ladle the stew into bowls and garnish with freshly chopped parsley. Serve immediately over mashed potatoes or with crusty bread on the side.