Preheat the oven to 400 degrees F. Spray a baking sheet with nonstick cooking spray.
Toss the sweet potatoes in a large bowl with the olive oil, 1/2 teaspoon salt and 1/4 teaspoon pepper. Transfer to the prepared baking sheet and bake for 20 minutes. Stir the potatoes and continue to bake until fork-tender, an additional 15 to 20 minutes. Let cool completely.
In a large bowl, combine the cooled sweet potatoes, arugula and scallions. In a small bowl, whisk the mayonnaise with the lemon juice and Parmesan; season with salt and pepper. Just before serving, toss the dressing with the sweet potato and arugula mixture to coat.