Cube the cream cheese and shred the cheeses if necessary. Let them sit at room temperature for 15 minutes. You’ll want them at room temperature when you add them to the pot.
Cook the chicken breasts:
Poaching: place them in a pot filled with water 3” higher than the chicken, bring to a boil, and once boiling, turn off the heat. Let it sit (poach) for 15 minutes. Pan searing: season with salt and pepper on both sides and cook in a pan for about 7 minutes per side. Slice or cube them right before you add them to the pasta. If using cooked rotisserie chicken, shred it or chop it into small pieces.
Cook:
Heat a large skillet over medium-high heat. Once hot, melt the butter and sauté the onions for 2 to 3 minutes, until they’re soft and translucent. Add the garlic and sauté it for about a minute. Add the can of diced tomatoes with the liquid and the chicken broth to the skillet and stir to combine.
Add the pasta to the liquid and bring it to a boil. Reduce the heat to low, cover, and cook for 10 to 12 minutes (check the pasta box). To ensure the pasta doesn’t stick, open the lid a few times throughout cooking and stir.
Once the pasta is al dente, not fully cooked but nearly there, add the Buffalo sauce, cream cheese, and Cheddar and Mozzarella cheeses. Stir to combine the cheeses and melt them into a creamy sauce. Once the sauce is cohesive, add the shredded chicken and stir to combine with the creamy pasta. This is a thick sauce. If you want to thin it out, add ¼ cup milk, broth, or water, and slowly mix it into the pasta.
Leftovers & Reheating:
Refrigerate leftovers for up to 3 days. To reheat, add 1 to 2 tablespoons of milk over the pasta, depending on how much you're heating up, to reconstitute the creamy sauce.