Season chicken breasts with salt and Italian seasoning. In a large Dutch oven or pot, melt butter over medium-high heat and sear the chicken until golden on both sides, about 3-4 minutes per side. Remove chicken and set aside.
In the same pot, add minced garlic and cook for 1 minute until fragrant, then add the chopped sun-dried tomatoes and cook for 2 minutes.
Pour in the chicken broth and bring to a simmer, scraping up any browned bits from the bottom of the pot.
Return the chicken to the pot, reduce heat to medium-low, cover, and simmer for 15-20 minutes until chicken is cooked through and tender.
Remove chicken to a cutting board and shred or dice into bite-sized pieces.
Stir the heavy cream and Parmesan cheese into the broth mixture until the cheese melts and the soup becomes creamy. Add red pepper flakes if using.
Return the shredded chicken to the pot and stir in fresh basil. Serve over rice or mashed potatoes in bowls.