Bring a large pot of water to a boil over high heat, add pasta and cook according to box instructions. Drain and return to the pot.
In another large pot add veggies and water. Bring to a simmer, cover and cook 10-12 minutes until veggies are easily pierced with a fork.
Transfer the veggies to a high speed blender with milk, melted butter and seasonings. Blend until completely smooth, stopping to scrape the sides as needed.
Pour blended veggie mixture into the pot with the pasta and turn on low heat. Add cheeses and stir until completely melted and smooth. Adjust seasonings as needed and serve hot.