Preheat the oven to 425°F (218°C). Using a sharp knife, halve the brussel sprouts length-wise. Peel and dice the butternut squash, removing the seeds.
Add the brussel sprouts, butternut squash, olive oil, nutmeg, cinnamon, salt, and pepper in a large bowl, and toss them together. Roast the vegetables on a baking sheet in the oven for 30 minutes, turning them over using a spatula about halfway through to ensure even browning.
While the veggies are roasting, melt the butter in a small pot or pan over medium-low heat. Add the soy sauce, maple syrup, and Dijon mustard, and stir together until full incorporated. Turn off the heat and set to the side.
Once the veggies are done cooking, let them cool slightly and transfer them to a large bowl. Pour the dressing over the veggies, add the cranberries, nuts, and cheese, if using and toss together.