Heat 1-2 Tablespoons of oil in a skillet over medium-high heat and sear the chicken breasts for 2-3 minutes per side, until lightly browned. Then, transfer the chicken to your slow cooker.

In a bowl, whisk together chicken broth, heavy cream, sun-dried tomatoes, garlic, thyme or oregano, and cornstarch. Pour the mixture over the chicken in the slow cooker.

Cover and cook the chicken on the low setting for 5-6 hours, or until the chicken is fully cooked and tender. Avoid lifting the lid during cooking.

For a super smooth sauce, use an immersion blender or regular blender to blend the sauce after cooking. Remove the chicken, blend the sauce until smooth, then return the chicken to the slow cooker.

Once the sauce has thickened, stir in the Parmesan cheese. Let the sauce simmer for an additional 5 minutes before serving. Garnish with fresh basil and extra Parmesan.