Position rack in center of oven and preheat the oven to 375 degrees F.
On a cutting board, cut the squash in half lengthwise. An adult may have to do this, since the squash is both very hard and round. Be very careful! Scrape the seeds and fibers from the squash with a spoon. Cut each squash half in 2 and place the quarters in a baking dish so that they fit in 1 layer, skin side down.
In a small mixing bowl, combine the butter, maple syrup, brown sugar, cinnamon, allspice, cloves, nutmeg, and a pinch of salt. Mix until smooth with a rubber spatula. Divide the butter mixture among the squash quarters, about 1 tablespoon each. Season the squash evenly with the remaining 1/4 teaspoon of salt and the black pepper. Butter mixture will melt inside the scooped-out squash wells. Cover the baking dish tightly with aluminum foil. Bake, covered, until the squash can be easily pierced with a fork, about 45 minutes.
Using oven mitts or pot holders, remove the baking dish from the oven and carefully remove the foil. Watch out for steam! With a pastry brush, brush the melted butter from the squash wells evenly over the inside of each squash. With oven mitts or pot holders, return the baking dish to the oven and bake, uncovered, for 20 to 30 minutes, or until the squash is golden brown around the edges.
Using oven mitts or pot holders, remove the dish from the oven. Using a slotted spoon, carefully transfer the squash to serving plates and serve immediately.