Set out the cheddar, mozzarella, and cream cheese to soften to room temperature before starting.
Place the chicken breast in a pot filled with water and bring it to a gentle simmer. Cook for about 15 minutes until fully cooked and tender.
Remove the chicken from the pot and use two forks to shred it finely. Toss the shredded chicken with the blue cheese dressing and keep aside.
In a large deep skillet, melt half the butter over medium heat. Add the diced onion and celery, cooking them until they soften, about 5 minutes. Then, stir in the garlic and cook for an additional minute.
Pour in the undrained diced tomatoes and the chicken broth, then bring the mixture to a boil.
Add the penne pasta to the boiling liquid, pressing it down to submerge completely. Wait for it to return to a boil.
Cover the skillet, reduce heat slightly, and let the pasta cook for 10 to 13 minutes until it is just al dente. Stir gently under the lid several times during cooking to prevent sticking and test pasta doneness before moving on.
Turn the heat down to low and stir in the buffalo sauce, cubed cream cheese, and both shredded cheeses gently until the sauce starts to become creamy, noting it will thicken further as it stands.
Mix in the shredded chicken and add red pepper flakes if desired for extra heat.
Optional: When the sauce is nearly as thick as you like, stir in the cold butter to finish the sauce with a glossy, smooth texture using the monter au beurre technique.
