Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper. Prepare the acorn squash by scrubbing it and slicing it into four 1-inch rings, starting at the bottom of the squash and working towards the top. You may find that depending on the size of your squash, you will cut more than four rings. Feel free to use a few more eggs to make more eggs-in-a-hole if you desire.
Use a spoon to remove the seeds from the rings and place them on the lined baking sheet. Season with salt and pepper if desired and bake for approximately 15 minutes or until tender when touched with a fork.
Remove from oven and carefully crack an egg into the center of each acorn squash ring. Return the baking sheet to the oven and bake for 10 minutes or until the yolks reach your desired hardness.
While the eggs-in-a-hole are cooking, prepare the sage brown butter. Melt the butter in a small saucepan, add the sage and lemon zest and let it simmer for 2 to 3 minutes.
When the eggs-in-a-hole are finished cooking, remove them from oven and transfer to plates for serving. Drizzle each serving with the sage brown butter and enjoy!
I chose to keep the skin on the acorn squash for some extra nutrients and fiber, but you can peel it if you want.