Heat a medium skillet with 2 Tbsp. of olive oil over medium heat. Season the chicken with salt and pepper. Then, brown each side for about 3-5 minutes. Next, pour in the water/broth, cover and continue cooking. For tenderloin, this will only take 3-4 minutes. For thicker chicken breasts, this will take around 10 minutes.
In a small bowl, whisk the hot sauce, lime juice, butter, and brown sugar. Set aside.
Brush olive oil on each side of the tortillas. Season with salt, then slice into strips. Place in a small skillet over low-medium heat and cook for 3-4 minutes per side, until browned.
Allow the chicken to cool before slicing. Meanwhile, pour about 2/3 of the hot sauce into the skillet and allow to bubble for 3-4 minutes. Next, add the sliced chicken and stir until well-coated.
Top salad greens with shredded carrots, pepper strips, cheese, Buffalo chicken, and tortilla strips. Use the extra hot sauce mixture as a dressing, if needed.