Preheat oven to 400 degrees. Cut butternut squash into 1 inch cubes and place them and broccoli florets on a cookie sheet. Drizzle with olive oil and salt and pepper. Bake for 20 minutes.
While your veggies bake, cook pasta and drain out water.
In large pan over medium-high heat add butter and garlic. Let melt. Add flour and whisk in until smooth. Cook for 2 minutes and then add milk and bring to a boil. Stir occasionally. Add nutmeg and cheese and stir until smooth.
In a blender, add milk mixture and cooked butternut squash. Blend until smooth. Pour over cooked pasta and stir until coated . Add broccoli and serve!