Preheat the oven to 425 degrees F., and line a baking sheet with parchment paper for easy clean up.

Remove the stems from the spaghetti squash, and then use a sharp knife to cut the squash from top to bottom (stem to blossom end lengthwise).

Use a spoon to scrape out the seeds inside the squash, and discard them (or feed them to your chickens!).

Place the squash, cut side down, on the parchment paper, and bake until tender, about 25 minutes.

While the squash is cooking, melt the butter in a small pan over medium to medium-high heat.

When the butter is melted, whisk in the flour, stir to combine, and cook for 30 seconds. Slowly whisk in the milk.

Add the salt, onion powder, and garlic powder. Stir to combine. Add the broccoli and let the mixture simmer for 1 or 2 minutes.

Add half of the cheddar cheese and half of the Swiss cheese, and stir until melted. Add the chicken and stir to combine. Remove from the heat, and set aside.

When the squash is done cooking, remove from the oven. Flip the squash over, and shred the flesh into "spaghetti" with a fork, taking care not to tear the skin of the squash.

Spoon the broccoli mixture evenly over the 4 pieces of squash, and then top with remaining cheese.

Bake for an additional 10 minutes, until the cheese is melted and bubbly.

Serve hot.