Preheat the oven to 375° F. Cut the squash in half vertically and scoop out the seeds. Rub inside of flesh with ½ tablespoon olive oil and 2 big pinches of salt. Place cut side down on a sheet pan and roast for 12 minutes. Turn over so cut side is facing up and bake for another 15-20 minutes, or until flesh is softened.
While squash is roasting, heat a cast iron skillet over medium heat. Add remaining olive oil and bring to medium high heat. Add onion and garlic to pan and sauté over medium heat for 3 minutes, until translucent. Stir in mushrooms and a big pinch of salt, cook for 4-5 minutes until softened and cooked through. Add kale and about 1 tablespoon water. Cook for about 3 minutes, until kale is wilted.
Remove the spaghetti squash from the oven when the strands will pull away from the outer skin. Be sure not to overcook. Remove from the oven and use a fork to remove the strands. Place them in a towel and squeeze some of the water out.
Add the spaghetti squash to the cast iron pan and use a fork to gently stir and combine, so kale distributes itself through the squash. Stir in the vinegar, black pepper and 2 big pinches of salt. Taste and adjust salt as needed.
Make wells in the middle of the hash and crack the eggs into them. Cook on medium heat until the yolk is as set as you prefer. Enjoy!