Pat the chicken completely dry with paper towels. Season both sides with salt, pepper, garlic powder, Italian seasoning, and red pepper flakes.
Pour sun-dried tomato oil into the base of the slow cooker. Add minced garlic and chopped sun-dried tomatoes. In a separate bowl, whisk cornstarch into the cold chicken broth until completely smooth with no lumps. Pour the cornstarch-broth mixture over the garlic and tomatoes and stir to combine.
Place seasoned chicken pieces into the slow cooker in a single layer. Do not stack.
Cover and cook on LOW for 3 to 4 hours or HIGH for 1.5 to 2 hours until the internal temperature reads 165°F / 74°C at the thickest point.
Remove chicken to a plate and tent loosely with foil. Warm the heavy cream in the microwave for 30 seconds until just warm. Pour warmed cream into the slow cooker and whisk it into the sauce. Add Parmesan in three separate additions, stirring after each until the sauce is smooth and glossy.
Return chicken to the slow cooker. Spoon sauce generously over each piece. Switch to the warm setting and rest for 5 minutes.
Turn the slow cooker off completely. Add torn fresh basil leaves. Stir gently once. Serve immediately over pasta, mashed potatoes, or with crusty bread.