Set the Instant Pot to Sauté and heat 1 tablespoon extra virgin olive oil for about 1 minute.
Season both sides of the chicken breasts evenly with 1/2 teaspoon kosher salt and 1/2 teaspoon ground black pepper.
Working in batches as needed, brown the chicken in the hot pot for about 2 minutes per side until golden, then transfer to a plate.
Add 1 tablespoon minced garlic, 1 teaspoon Italian seasoning, and 1/4 teaspoon crushed red pepper flakes to the pot and cook while stirring for about 30 seconds until fragrant, then press Cancel.
Pour in 1/2 cup low-sodium chicken stock (or 3/4 cup for an 8-quart model) and scrape up any browned bits from the bottom with a wooden spoon or spatula.
Return the seared chicken to the pot, add the drained and roughly chopped 7 oz jar of oil-packed sun-dried tomatoes and a pinch of salt, then pour in 1 cup heavy cream.
Secure the lid, set the valve to sealed, and cook on Manual/Pressure Cook at high pressure for 5 minutes.
When the timer ends, allow the pressure to release naturally for at least 10 minutes, then perform a quick release if needed and open the lid.
Remove the chicken to a clean platter. Press Cancel, then set the pot to Sauté; stir in 1/2 cup grated Parmesan and 2 cups baby spinach and cook until the spinach wilts and the sauce thickens, about 2–3 minutes.
Serve the sauce spooned over the chicken and top with additional Parmesan or basil if desired.