Combine the squash, and milk, in a medium saucepan. Bring it to a boil over medium-high heat, being careful not to scorch the milk. Reduce heat to medium, and simmer until squash is tender when pierced with a fork, about 25 minutes. Remove from heat.
Blend the milk and squash until its smooth. While it’s still hot, add in the 9 ounces of cheese.
Cook the pasta, with the cauliflower according to package directions, and drain well.
Combine the pasta and cauliflower mixture with the squash mixture, in a dutch oven.