Season the chicken breasts with salt, pepper, and garlic powder on both sides.
Heat butter and olive oil in a skillet over medium-high heat.
Lightly sear the chicken breasts.
Transfer the chicken, along with the oil and butter from the skillet, to your crockpot.
In a mixing bowl, whisk together chicken broth, heavy cream, garlic, and the remaining seasonings.
Pour this mixture over the chicken in the crockpot.
Add the sun dried tomatoes.
Cook on low for 4 hours, until the chicken reaches an internal temperature of 165°F.
Remove the chicken and place it on a plate.
Whisk the sauce in the crockpot and add freshly grated parmesan cheese. If you want to thicken the sauce, combine 1 tablespoon cornstarch and 2 tablespoon water to make a cornstarch slurry to add to the crockpot.
If using cornstarch, cover the chicken and turn the crockpot to high for 10 more minutes.
Return the chicken to the crockpot and top with fresh basil.
Serve, over noodles, rice, or mashed potatoes.