Preheat oven to 400°F. Line a baking sheet with foil, place bacon on sheet and cook in the preheated oven for 8 minutes, or until crispy. Remove from oven and allow to cool. Crumble into small bits and set aside.
Bring a pot of salted water to a boil. Add pasta and cook until al dente. Drain pasta and place back into the pot.
While pasta is cooking, melt butter in a medium saucepan set over medium-high heat. When melted, add flour and cook for 2 minutes, stirring constantly. Add milk and squash puree and cook until thickened. If the sauce is too thick add milk, ¼ cup at a time, until it reaches desired thickness.
Add cheese and nutmeg to the sauce and stir until cheese is melted. Season with salt and pepper.
Pour sauce over cooked pasta, add crumbled bacon, reserving a small amount. Mix well to combine, serve in bowls and garnish with remaining bacon. If desired, sprinkle breadcrumbs over pasta and bake in a 350°F oven for 10 minutes.
Peel squash and slice in half lengthwise. Using a large spoon, remove seeds and discard. Chop squash into 1” cubes and place in a medium saucepan. Add sage and cover with stock.
Bring to a boil. Cover and reduce heat to low and simmer for 15–20 minutes or until squash is fork-tender.
Remove pot from stove and puree squash using an immersion blender.