Place chicken in a casserole dish. In a small bowl, combine pickle juice, salt, and minced garlic. Pour over the chicken and brine for 1 hour.
Preheat the smoker to 225 degrees F.
Peel away all the loose layers on the garlic. Cut the top ¼” off the bulb to expose the cloves inside. Pour olive oil over the cloves and season with salt. Place onto a small cast iron skillet and set aside until the chicken goes into the smoker.
Combine all chicken rub seasoning ingredients in a small bowl and mix.
Remove chicken from the brine and pat dry with a paper towel.
Season both sides of the chicken generously with the rub.
Place chicken breasts onto a baking sheet. Add the chicken and garlic to the smoker and close the lid.
Remove the garlic from the smoker at the 1 hour mark.
Gently squeeze the garlic out of the bulb and into a small bowl. Mash using a fork.
Melt butter in a small saucepan over medium heat. Once melted, add the roasted garlic, hot sauce, and honey. Whisk to combine and cook for 5 minutes.
Combine cornstarch and water in a separate bowl. Whisk, then pour into the saucepan.
Stir sauce and continue cooking for 5 minutes to thicken.
Remove chicken from the smoker at the 90 minute mark. *keep the smoker on*
Add chicken to a Dutch oven. Pour chicken broth inside and place back into the smoker. *Do not use the lid on the Dutch oven*. Place the honey garlic saucepan into the smoker. Smoke for 30 minutes. (This will keep the sauce warm and infuse it with more smokey flavor)
Shred the chicken, then pour the honey garlic sauce inside and toss to coat. Place onto a baking sheet and return to the smoker. Smoke for 45 more minutes.
Serve pulled chicken on a sandwich with coleslaw or on its own with veggies.