Preheat your oven to 400 degrees F.
Cut the squash in half, remove the seeds, and place, face down on, a baking sheet.
Bake for 30 minutes, then remove from the oven, and set aside to cool.
Remove the flesh of the squash using a fork and set aside in a bowl.
Melt some cooking fat in a skillet placed over a medium-high heat.
Sauté the onions and garlic until the onions are soft.
Add the asparagus and mushrooms; continue cooking until the asparagus is starting to get soft but still crunchy (watch for the moment it starts to change color).
In a bowl, whisk together the eggs, coconut milk, rosemary, and season with salt and pepper to taste.
Make the “crust” of your quiche by lining a deep pie dish with the cooked spaghetti squash, pressing gently on the bottom and sides to make it even.
Pour the egg mixture over the squash and add the asparagus and mushrooms on top of the eggs.
Place in the oven and cook for 40 minutes.