Place the butternut squash on a sheet pan. Drizzle with 2 tablespoons olive oil, the maple syrup, 1 teaspoon kosher salt and ½ teaspoon black pepper. Toss to evenly coat the butternut squash. Roast for 20 minutes, turning once, until the squash is tender. Add the cranberries to the pan during the last 5 minutes.
While the squash is roasting, combine the apple cider, the vinegar and the 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 ¼ cup. Off the heat, whisk in the mustard, ½ cup olive oil, 1 teaspoon kosher salt and ½ teaspoon ground black 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.