Preheat oven to 400 degree F. Line a baking sheet with parchment paper.
With a knife, carefully score squash lengthwise where you’re going to cut it in half. Poke a few holes along the score.
Microwave the squash for 5 minutes or until the scored skin is soft enough to cut. Allow to cool.
Carefully cut the squash in half. Scoop out the seeds.
Brush the inside of both halves of the squash with olive oil. Season with salt and pepper.
Place the two halves cut side down on the prepared pan and roast until tender, about 30 minutes. Allow several minutes to cool.
Using a fork, scrape the insides to create a spaghetti-like texture. Leave insides in the squash.
Sprinkle bacon and cheese on top of the fluffed squash. Make 2 wells in each half and break an egg in each well.
Place breakfast squash halves back in the oven, and bake until egg whites are set and yolks are starting to thicken, about 10-15 minutes, depending on how you like your baked eggs to be.
Garnish with chopped green onion and black pepper.