Prep the oven and squash seasoning: Preheat the oven to 400°F.
Toss the squash: Place the butternut squash on a baking sheet. Drizzle it with maple syrup and 2 tablespoons of olive oil. Sprinkle it with 1 teaspoon kosher salt, and ½ teaspoon black pepper. Toss to ensure that all of the butternut squash is coated.
Roast and turn: Place it in the oven and roast for 20-25 minutes until tender, turning once halfway through. In the last 5 minutes, add the cranberries.
Make the vinaigrette: Place apple juice, cider vinegar, and minced shallots in a small saucepan and bring to a boil over medium-high heat. Cook for 6-8 minutes, or until reduced to 1/4 cup. Remove from heat.
Finish the dressing: Off the heat, whisk in the Dijon mustard, 1/4 cup of olive oil, 1 teaspoon salt, and 1/2 teaspoon pepper. Whisk until emulsfied.
Assemble the salad: Place the arugula (or salad greens) in a large salad bowl. Pour over the dressing and give it a big toss. Add the roasted butternut squash and cranberries.
Finish and serve: Top it off with toasted walnuts and shaved Parmesan cheese. Taste and season with salt and pepper, if necessary. Enjoy!