Set the Instant Pot to Sauté and heat 1 tablespoon extra virgin olive oil in the inner pot for about 1 minute.
While the oil heats, season both sides of the chicken breasts with 1/2 teaspoon kosher salt and 1/2 teaspoon ground black pepper.
Working in batches if needed, add chicken to the hot pot in a single layer and brown 2 minutes per side until golden; remove browned chicken to a plate and repeat with remaining pieces.
To the pot, add 1 tablespoon minced garlic, 1 teaspoon Italian seasoning and 1/4 teaspoon crushed red pepper flakes and cook, stirring, 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 the bottom with a wooden spoon to loosen any browned bits.
Return the seared chicken to the pot and add the drained, roughly chopped jar (7 oz) oil-packed sun-dried tomatoes and 1 cup heavy cream.
Secure the lid and set to Manual/Pressure Cook on HIGH for 5 minutes. When the cook time ends, allow natural pressure release for at least 10 minutes, then quick-release any remaining pressure if needed.
Open the lid and transfer the chicken to a clean platter.
Press Cancel, then set to Sauté. Stir in 1/2 cup grated Parmesan and 2 cups baby spinach and cook 2–3 minutes until the spinach wilts and the sauce thickens; then press Cancel.
Serve the sauce spooned over the chicken; top with additional Parmesan or basil if desired.