Optional: Lightly season the chicken breasts with salt and pepper. Heat an oiled skillet over medium-high heat. Starting with the skin side down, brown both sides of the chicken, cooking about 3-5 minutes per side.
Lightly grease a 5 or 6 quart slow cooker. Transfer the chicken to the slow cooker.
In a mixing bowl, whisk together the basil, oregano, thyme, rosemary, ground mustard, cayenne, garlic, honey, vinegar, and chicken broth. Pour this mixture over the chicken.
Cover and cook until the chicken is cooked through and reaches an internal temperature of 165 F. This should take about 7-8 hours on low or 3 1/2 to 4 hours on high.
Optional: Transfer the chicken to a serving plater and cover to keep warm. Pour the cooking juice into a sauce pan or skillet. Reduce by half over medium-high heat to thicken the sauce, then drizzle over the chicken and / or sides.
Serve with a side salad, warm rice or crunchy bread, and enjoy!