Add ½ cup hot sauce, honey, garlic powder, onion powder, ½ teaspoon salt, and pepper to a large bowl. Whisk to combine. Add the chicken breast to the bowl and toss to coat. Cover with plastic wrap and refrigerate for at least 1 hour.
In a separate bowl, whisk together the 1 tablespoon of olive oil, apple cider vinegar, and remaining salt. Add the onion, carrots, and cilantro to the bowl. Mix to combine. Set aside.
Heat 2 tablespoons of olive oil in a large skillet over medium heat. When the oil is fragrant, add the chicken to the pan and cook for 5 minutes. Flip the chicken and cook for another 5-7 minutes, or until it reaches 165℉. Remove the chicken from the pan and set aside for 5 minutes.
Shred the chicken and place it into a bowl. Stir in the remaining buffalo sauce.
To assemble the quesadilla, place ⅓ cup of shredded cheese on one side of a tortilla. Scoop ⅓ -½ cup of shredded buffalo chicken on top of the cheese. Finally, place ¼ cup of the carrot mixture on the chicken. Fold the tortilla in half.
Heat another skillet over medium heat. Brush the remaining olive oil on the outside of each assembled quesadilla. Cook each quesadilla for 1-2 minutes on each side. Remove from heat once the sides are golden brown and set aside.
Serve with blue cheese or ranch dressing.