Preheat oven to 400F.
Slice spaghetti squash in half, lengthwise. Scoop out seeds Place open side down on a cookie sheet with about 1/4th inch of water. Bake spaghetti squash for approximately 30 min, or until outer shell is soft to the touch. Remove from oven and let cool.
Shred spaghetti squash with a fork and wrap in paper towel and squeeze to remove excess water.
Combine squash and boiled, shredded chicken in a large bowl and mix well. Add hot sauce and Greek yogurt, followed by eggs, making sure to mix thoroughly.
Layer 1/2 of the squash and chicken mixture in a casserole dish. Spread broccoli evenly across the top, then continue with the sharp cheddar cheese. Layer the second half of the squash and chicken mixture evenly across the broccoli, then top with sharp white cheddar.
Bake for 30 min. Remove and allow to cool for 5-10 minutes before serving. Add salt and pepper to taste and enjoy!