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Preheat the oven to 400 degrees F.
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Place the butternut squash on a sheet pan. Add 1 tablespoons olive oil, maple syrup, 1/2 tsp salt and 1/2 teaspoon pepper and toss. Roast the squash for 15 to 20 minutes, turning once during cooking, until tender.
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Combine the cranberry juice, vinegar, and shallots in a small saucepan and bring to a boil over medium-high heat. Cook for 5- 6 minutes, until the liquid is reduced to about 1/4 cup.
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Turn the heat off and whisk in the mustard, 2 tbs cup olive oil, 1/4 tsp salt and 1/2 teaspoon of pepper.
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Place the arugula in a large salad bowl and add the roasted squash mixture, the walnuts, and the grated Parmesan. Add just enough vinaigrette to moisten the salad and serve immediately.