Season chicken with salt and pepper. Heat olive oil and butter in a skillet over medium heat, then sear chicken for 2-3 minutes per side until lightly golden. Transfer to the slow cooker along with any leftover butter and juices from the skillet.

In a bowl, whisk chicken stock with cornstarch, garlic, crushed red pepper, oregano, and thyme. Pour the mixture over the chicken in the slow cooker.

Top each chicken breast with the chopped sun-dried tomatoes. Cover and cook on low for 3-4 hours or on high for 1.5-2 hours, until chicken reaches 165°F (74°C).

Remove chicken to a plate and keep warm. Stir heavy cream and parmesan into the hot liquid in the slow cooker until smooth. Return chicken to the sauce, spoon sauce over the top, and let rest for 5-10 minutes on 'warm'.

Garnish with basil before serving.