Turn the Instant Pot to sauté, add 1 tablespoon extra virgin olive oil to the inner pot, and heat for 1 minute. While the oil is heating, evenly season both sides of 4-6 boneless, skinless chicken breasts with ½ teaspoon kosher salt and ½ teaspoon ground black pepper.
Working in batches if needed, place the seasoned chicken in a single layer in the instant pot, and brown for 2 minutes per side, or until golden. Once browned, remove the chicken to a plate. Repeat the process with any remaining chicken breasts if needed.
Add 1 tablespoon minced garlic, 1 teaspoon Italian seasoning, and ¼ teaspoon crushed red pepper flakes to the inner pot, and cook for 30 seconds or until fragrant. Hit cancel to turn off the pressure cooker.
Add ½ cup low-sodium chicken stock and use a wooden spoon or spatula to scrape up any browned bits off the bottom of the inner pot.
Add the seared chicken back to the inner pot. Add in the 1 (7 oz) jar oil-packed sun-dried tomatoes (drained), a pinch of salt, and 1 cup heavy cream.
Secure the lid and turn the knob to the sealed position. To set the cooking time, hit manual or pressure cook and set the cooking time for 5 minutes on high pressure.
Once the cooking time has elapsed, allow the pressure to release naturally for at least 10 minutes. After 10 minutes, you can opt to do a quick release of pressure (or allow pressure to release fully on its own).
Open the Instant Pot, and remove the chicken to a CLEAN platter.
Hit cancel to turn off the keep warm function, then hit sauté. Add in ½ cup grated parmesan and 2 cups baby spinach leaves and stir until the spinach is wilted and the sauce has thickened about 2-3 minutes. Hit cancel to turn off the sauté function.
Serve the sauce over the chicken with additional parmesan and basil if desired.