Preheat oven to 400° F. Line a large baking sheet with parchment paper.
Toss the squash with olive oil and kosher salt. Place the squash in a single layer on the prepared baking sheet.
Combine the bread crumbs, Parmesan, nutmeg, pepper, salt, garlic, and thyme in a bowl. Stir to mix well. Sprinkle this all over the squash and roast until tender, about 40 minutes. Garnish with chopped parsley and serve warm or at room temperature.