If desired, sear the chicken in a skillet with oil for 2-3 minutes per side until lightly browned. Transfer to the slow cooker.
In a bowl, whisk together chicken broth, heavy cream, sun-dried tomatoes, minced garlic, thyme or oregano, red pepper flakes, and cornstarch. Pour over the chicken.
Set the slow cooker to low and cook for 5 to 6 hours, until the chicken is tender.
If desired, blend the sauce for a smoother texture, then return the chicken to the slow cooker and stir to coat.
Add Parmesan cheese and simmer for an additional 5 minutes. Garnish with fresh basil before serving.
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Notes
Store leftovers in an airtight container for up to 3-5 days. Reheat gently on the stove or microwave.