Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper or aluminum foil.
Toss the squash cubes with the olive oil, salt, pepper and nutmeg. Spread them out on the baking sheet and bake for 15 minutes, then toss and bake for 15 more, or until tender when pierced with a fork.
Add the squash (and any olive oil drippings) to a food processor and blend until completely pureed and smooth. Once smooth, add the squash to a large bowl with the eggs and parmesan cheese. Whisk until combined and most of the lumps have been smoothed out.
While the squash is roasting, you can heat a large skillet over medium heat and add the bacon. Cook until totally crispy and the fat is rendered. At this time, you can also boil the water for the spaghetti and cook it.
Remove the bacon from the skillet with a slotted spoon and place it on a paper towel to drain the grease. Place the garlic in the skillet and cook for 1 minute. Add the spaghetti to the skillet and toss it well in the bacon fat with kitchen tongs – you want it to be throughly coated. Remove the skillet from the heat.
Pour in the squash/egg/parmesan mixture and stir quickly and constantly to create a creamy sauce, tossing for about 3 to 4 minutes or so. Stir in the bacon into the pasta and sprinkle with fresh herbs. Top with extra cheese. Taste and season additionally if you’d like. Serve immediately!