Place your chicken breasts, chopped onion, and minced garlic into your slow cooker.
In a medium bowl, use a whisk to mix together your bourbon, chicken broth, brown sugar, soy sauce, lemon juice, tomato paste, and ground ginger. Then pour this mixture over the chicken in the slow cooker.
Cover your slow cooker, set the temperature on low, and cook for six to seven even hours (or high for three to four hours.
Check on the chicken periodically while it is slow cooking. If the sauce seems thin, you can remove the chicken during the last 30 minutes of cooking and set it aside. Then in a small bowl, whisk the cold water and cornstarch together and add it to the sauce in the slow cooker, stirring thoroughly.
Your chicken is done slow cooking when it is 'pull-apart tender' and reaches an internal temperature of at least 165℉.
When your chicken has finished cooking, carefully use two forks to shred it. You can transfer the chicken to a work area, such as a cutting board, to do this and then return it to the slow cooker.
Stir the chicken and sauce in the slow cooker so that the chicken is well covered with the sauce. Then serve as desired.