Season the chicken: Pat the chicken breasts dry with paper towels and season both sides with salt, pepper, and Italian seasoning. This helps the seasoning stick and flavors the meat from the inside out.
Build the sauce base: In the crockpot, whisk together the chicken broth, chopped sun-dried tomatoes, and minced garlic until combined. This liquid will simmer with the chicken and become the base of the sauce.
Add the chicken: Nestle the seasoned chicken breasts into the broth mixture, making sure they're mostly submerged. Spoon a little of the liquid over the top of each piece.
Cook low and slow: Cover and cook on low for 5 to 6 hours or on high for 3 to 4 hours, until the chicken reaches 165°F internally and shreds easily with a fork.
Remove the chicken: Transfer the cooked chicken to a plate and tent loosely with foil to keep warm while you finish the sauce.
Stir in the cream: Pour the heavy cream and parmesan cheese into the liquid left in the crockpot, stirring until the cheese melts smoothly into the sauce.
Thicken the sauce: Whisk the cornstarch with the water to make a slurry, stir it into the sauce, and let it cook uncovered on high for about 10 minutes until it thickens enough to coat a spoon.
Return the chicken: Slice or shred the chicken as you like, then return it to the thickened sauce and spoon the sauce over the top to coat each piece.
Add fresh basil: Stir in the chopped fresh basil just before serving so it keeps its bright color and flavor.
Serve warm: Spoon the chicken and sauce over your favorite side, garnish with extra basil and parmesan, and serve immediately.