Prep chicken: Pat chicken breasts dry with paper towels. Season both sides with salt, pepper, and Italian seasoning.
Sear chicken: Set Instant Pot to SAUTÉ mode. Add olive oil. When hot, add chicken breasts and brown for 2-3 minutes per side. Work in batches if needed. Remove chicken and set aside.
Create flavor base: With pot still on SAUTÉ mode, add minced garlic and cook for 30 seconds until fragrant. Pour in chicken broth, scraping all browned bits from bottom of pot. Add chopped sun-dried tomatoes and red pepper flakes.
Pressure cook: Return seared chicken to pot. Close lid, set valve to SEALING, and cook on HIGH PRESSURE for 8 minutes. When cooking completes, allow 5-minute natural pressure release, then carefully release remaining pressure.
Finish sauce: Remove chicken and set aside covered with foil. Switch to SAUTÉ mode, add heavy cream and bring to gentle simmer. Stir in parmesan cheese until melted and smooth. Let sauce simmer 2-3 minutes until slightly thickened.
Serve: Return chicken to pot to warm through. Serve topped with sauce and garnished with fresh basil. Pair with pasta, crusty bread, or vegetables.