Preheat a gas grill to medium-high heat, aiming for around 400°F (205°C).
Clean the grill grates with a brush and lightly oil them with a paper towel dipped in vegetable oil.
If using charcoal, let it burn until it turns ashy white. Spread the coals out evenly, clean the grates, and lightly oil them.
Rinse the acorn squash under cold water to remove dirt, and then pat it dry with a paper towel.
Cut the acorn squash in half lengthwise, then scoop out the insides (seeds and stringy bits) with a spoon or ice cream scooper. Place squash cut-side down on a cutting board and slice into 1-inch slices, wedges, or desired shape. Try to keep them uniform so they cook evenly.
Arrange the squash slices in a single layer on your prepared baking sheet.
Mix cinnamon, ginger, nutmeg, salt, and chili pepper in a small bowl. Set aside.
Brush each slice with half the melted butter, spice mixture, and optional salt.
Once the grill is hot, place the acorn squash slices directly on the grill grates. Cook for 4-5 minutes on one side.
Then, flip the squash halves on the other side. Brush each half with maple syrup and continue grilling until tender, 5 minutes or more, depending on the size of the squash.
Remove and sprinkle with brown sugar and nuts for sweet squash or herbs for a savory side.