Preheat oven to 375 degrees.
Fill a large saucepot 3/4 full with salted water and place on high heat (like you're making pasta). Once boiling, drop in the squash andand cook for 4-5 minutes to soften. Scoop out the squash and add in the short cut pasta. Cook pasta to very al dente, 2 minutes shy of package directions.
As pasta cooks, add squash to your blender, along with the milk, cornstarch, dijon, and 1/2 teaspoon of salt. Liquify.
Set an ovensafe pan (like your cast iron or dutch oven, needs to be big enough to hold the pasta later) over medium heat. Add in oil, garlic, black pepper, and 1/2 teaspoon of salt, and cook for one minute. Once garlic is softened, stir in squash mixture and cheese, and bring to a simmer.
Once sauce is simmering, fold in the pasta. Top with the parmesan and bake uncovered for 15 minutes. Serve as soon as you don't burn your mouth.