Preheat the oven to 400 °F degrees.
Mix maple syrup, 2 tablespoons of olive oil, 1-teaspoon salt, 1/2 teaspoon black pepper in a small cup.
Place the butternut squash on a baking pan. Pour the maple syrup and olive oil mixture over it. Using your clean hands, toss it to ensure that all the butternut squash is coated with it.
Place it in the oven and roast it for 20 minutes. Half way through, using a spatula, turn the butternut squash to make sure it roasts evenly. In the last 5 minutes add the cranberries to the pan.
In the mean time make the vinaigrette. Place apple juice, cider vinegar and minced shallots in a small saucepan and cook in medium-high heat for 10-13 minutes until it is reduced to 1/4 cup.
Once ready, off the heat, whisk in the Dijon mustard, 1/4 cup of olive oil, 1 teaspoon salt and 1/2 teaspoon.
Place the salad greens (or arugula) in a large salad bowl. Add the roasted butter squash and cranberries.
Drizzle it with the vinaigrette. Give it a big toss. Taste and season it with salt and pepper, if necessary.
Top it off with toasted walnuts and grated Parmesan cheese.