Add the dressing ingredients to the bowl of a mini food processor. Blend until well combined. Alternatively, add the ingredients to a mason jar and shake well. Set aside.
Preheat the oven to 375 degrees.
Preheat an oven-safe skillet over medium heat. Season both sides of the chicken with salt and pepper.
Add ½ tablespoon butter to the skillet. Add the chicken and cook for 3-4 minutes until golden brown. Flip and cook another 1-2 minutes. Transfer the skillet to the oven and cook for 10-15 minutes or until the internal temperature reaches 165 degrees. The amount of time will depend on the thickness of the chicken. Let the chicken rest for 5 minutes.
While the chicken cooks, add the buffalo sauce, brown sugar, and butter to a small saucepan. Heat over low heat until the butter melts and the sauce is heated through.
Toss the chicken in the sauce and then slice.
Add the romaine lettuce and croutons to a large bowl. Add ½ cup of the Caesar dressing and toss to coat. Add more dressing as needed or serve the extra on the side. Transfer the salad to two plates or bowls.
Top each salad with one sliced chicken breast. Garnish with Parmesan cheese and blue cheese. Serve immediately.
Notes
To clean romaine lettuce, cut off the core end. Slice the lettuce cross-wise in one-inch pieces. Add the lettuce to a salad spinner and rinse thoroughly with cold water. Spin dry and chill.