In a bowl, mix syrup, vinegar, lemon juice, vanilla and bourbon together. Cup acorn squash in half and brush mixture on top with a pastry brush. Set squash cut side up in a baking dish. Bake for 20 minutes.
Remove from oven and brush mixture over squash again. Pour remaining mixture into each squash cavity equally. Top with 1 tablespoon butter each and a sprinkle of nutmeg. Bake for 20 more minutes.