Clean the grill grates, dip a paper towel into vegetable oil, and oil the grates.
If using a gas grill, preheat it on medium-high heat until it reaches around 400°F (205°C). For charcoal, let it burn until it turns ashy white, and spread the coals out evenly.
Rinse the squash to remove dirt and debris, and then pat them dry.
Cut them in half lengthwise and scoop the seeds and stringy bits out with a spoon. Place the squash cut-side down on a cutting board and slice into 1-inch wedges or other desired shape, making them as uniform as possible so they cook evenly.
Arrange the slices in a single layer on a greased and parchment-paper-lined baking sheet.
Melt the butter, then mix the cinnamon, nutmeg, ginger, and red pepper in a small bowl.
Brush the slices with half the melted butter, sprinkle on the desired amount of spice mixture, and sprinkle with a little optional salt.
Once the grill is hot, place the slices right on the grates and grill them for 4-5 minutes on one side.
Flip them onto the other side, brush the slices with butter and maple syrup, and continue grilling until tender (about 5 minutes, depending on the thickness).
Remove from the grill, garnish with the chopped nuts, and serve with the rest of the melted butter and maple syrup on the side.