1. Preheat the oven to 400 degrees F. Line a baking sheet with heavy-duty foil.
2. Put the sweet potatoes on the foil, drizzle with half of the oil and sprinkle with half of the celery salt and red pepper flakes. Turn with a spatula to coat. Roast until the potatoes are tender and beginning to shrivel, about 20 minutes.
3. While the potatoes are roasting, toss the asparagus with the remaining oil, celery salt and red pepper flakes in a medium bowl. Using a spatula, add the asparagus pieces to the sweet potato pan and toss to combine. Cook until the asparagus softens and the tips begin to brown, another 10 minutes. Sprinkle the Parmesan over the vegetables and cook until the cheese just melts and coats the vegetables, another 5 minutes. Spread the vegetables on a serving platter and sprinkle with the chopped parsley. Serve warm.