Add cream cheese, cheddar, and ½ cup mozzarella (1 pack) to pan and whisk until smooth (we’ll use the rest of the mozzarella later). Season with salt and pepper. Thinly slice chicken. Drain broccoli. Stir chicken, broccoli, and cavatappi into pan. Season with salt and pepper. (TIP: If your pan isn’t ovenproof, transfer mixture to a baking dish at this point.) Place 1 TBSP butter in a small, microwave-safe bowl. Microwave on high until it melts, about 45 seconds.