Preheat your oven to 400°F (200°C). On a large baking sheet, toss the butternut squash cubes with 2 tablespoons of olive oil, the maple syrup, 1/2 teaspoon of salt, and 1/4 teaspoon of pepper. Spread into a single layer.
Roast the squash for 15 to 20 minutes, flipping halfway through, until it is tender and lightly caramelized. Add the dried cranberries to the baking sheet for the last 5 minutes of roasting.
While the squash roasts, make the vinaigrette. In a small saucepan, combine the apple cider, cider vinegar, and minced shallot. Bring to a boil over medium-high heat.
Cook for 6 to 8 minutes, until the liquid has reduced to about 1/4 cup. Remove the saucepan from the heat.
Whisk the Dijon mustard, the remaining 1/2 teaspoon of salt, and the remaining 1/4 teaspoon of pepper into the reduced cider mixture. Slowly drizzle in the 1/2 cup of olive oil while whisking continuously until the vinaigrette is emulsified.
In a large salad bowl, combine the baby arugula, toasted walnuts, and Parmesan cheese.
Add the warm roasted squash and cranberry mixture to the bowl. Drizzle with about half of the vinaigrette and toss gently to combine. Add more vinaigrette as needed to coat the salad lightly. Serve immediately.