Preheat the oven to 400 degrees F. Cut squash in half, scoop out the seeds and pulp, remove rind, and cut into 1 inch pieces. Place the squash on a baking sheet and sprinkle with olive oil, maple syrup, salt and teaspoon pepper and mix to coat well. Put in preheated oven and roast for 10 minutes, turn, and roast an additional 10 to 15 minutes or until tender and browning. Just before roast cooks completely, sprinkle cranberries on top and put back in oven for final minutes - about 2 or 3 minutes is enough.

Meanwhile, in a small saucepan, whisk together the apple juice, apple cider, and shallots and bring to a boil over medium heat; cook until this liquid is reduced to about 1/4 cup, for about 5 to 10 minutes. Remove from heat and whisk in the Dijon mustard, 1/2 cup olive oil, 1 teaspoon salt, and 1/2 teaspoon pepper to make the vinaigrette dressing. To assemble, put the arugula in a large salad bowl and add the roasted squash mixture, walnuts, and Parmesan. Drizzle a little vinaigrette over the salad and toss to combine. Add more vinaigrette if desired, taste, and add more kosher salt and pepper if needed. Serve immediately. Will serve about 4 to 6 people.