Preheat the oven to 400 degrees F.
Place 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.
While 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.
Place 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. Sprinkle with salt and pepper and serve immediately.
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