Season the chicken: Pat the chicken breasts dry and season both sides with kosher salt, black pepper, and Italian seasoning.
Sear the chicken: Set the Instant Pot to Sauté and add olive oil. Brown the chicken in batches, giving each piece enough space to sear properly. Transfer the browned chicken to a plate.
Build the sauce base: Add butter and minced garlic to the pot. Cook briefly until fragrant, then stir in tomato paste, chopped sun-dried tomatoes, and red pepper flakes.
Deglaze the pot: Pour in the chicken broth and use a wooden spoon to scrape all the browned bits from the bottom. This helps develop the sauce and reduces the chance of a burn warning.
Pressure cook: Turn off Sauté and return the chicken and any collected juices to the pot. Lock the lid and cook on High Pressure for 8 minutes.
Release the pressure: Let the pressure release naturally for 5 minutes, then carefully release the remaining pressure.
Check the chicken: Remove the lid and check the thickest part of the chicken with a food thermometer. It should reach 165°F (74°C).
Finish the creamy sauce: Remove the chicken from the pot. Set Sauté to low, add the heavy cream, and gently simmer for a few minutes.
Add Parmesan: Turn off Sauté and gradually stir in the freshly grated Parmesan until the sauce becomes creamy and smooth.
Combine and serve: Return the chicken to the sauce and spoon the creamy sauce over the top. Finish with fresh basil and serve warm.