Preheat your oven to 400°F (200°C). Slice each honeynut squash in half lengthwise and scoop out the seeds. Arrange the halves cut-side up on a baking sheet, drizzle with olive oil, and season with salt and pepper. Roast for 30-35 minutes or until tender.
Once roasted, allow the squash to cool slightly. Scoop out the flesh from 6 of the squash halves (these will be discarded). For the remaining 6 halves, scoop out the flesh, leaving a thin layer inside the shell to keep them intact.
In a bowl, mash the scooped-out squash flesh. Add 1/2 cup goat cheese, rosemary, nutmeg, thyme, salt, and pepper. Mix until smooth and well-combined.
Fill each squash shell with the goat cheese mixture, spooning it in generously.
Place a slice of Gruyère cheese over each stuffed squash half.
Switch your oven to the broil setting. Place the stuffed squashes under the broiler for 2-4 minutes, or until the Gruyère melts and turns golden brown.
Remove from the oven, and top with additional thyme and freshly cracked black pepper before serving. Enjoy this dish as a perfect fall side!