Bring a large pot of salted water to a boil and cook the elbow macaroni until al dente. Drain and set aside.
Remove the skin and bones from the cooked chicken and shred the meat into bite-sized pieces.
In a large Dutch oven or heavy pot, melt the butter over medium heat.
Whisk in the flour and cook for about 1 minute until lightly golden.
Gradually pour in the milk while whisking continuously until the sauce thickens, about 5–6 minutes.
Season with black pepper.
Stir in the Cheddar and Monterey Jack cheeses until completely melted and smooth.
Add the buffalo hot sauce and stir well. Taste and adjust the spice level if desired.
Fold in the blue cheese (or extra Cheddar), shredded chicken, and cooked macaroni.
Stir until everything is evenly coated in the creamy sauce.
Serve the Buffalo Chicken Mac and Cheese immediately while hot. Garnish with chopped parsley, green onions, or extra cheese if desired.