1Preheat the oven to 400F.
2Place the butternut squash on a sheet pan. Add 2 tablespoons olive oil, the maple syrup, 1 teaspoon salt and 1/2 teaspoon pepper and toss. Roast the squash for 15 to 20 minutes, turning once, until tender. Add the cranberries to the pan for the last 5 minutes.
3While the squash is roasting, combine the apple cider, vinegar, and shallots in a small saucepan and bring to a boil over medium-high heat. Cook for 6 to 8 minutes, until the cider is reduced to about 1/4 cup. Off the heat, whisk in the mustard, 1/2 cup olive oil, 1 teaspoon salt, and 1/2 teaspoon of pepper.
4Place the arugula in a large salad bowl and add the roasted squash mixture, the walnuts, and the grated Parmesan. Spoon just enough vinaigrette over the salad to moisten and toss well.
5 Sprinkle with salt and pepper and serve immediately.