Whisk the olive oil and Dijon mustard together in a large bowl. Add the cut fingerlings, sweet potatoes (or squash), and red onion rings. Toss with your hands to fully coat. Then divide the vegetables between 2 large rimmed baking sheets coated with cooking spray. Pile the vegetables at the center of each baking sheet to start.
Sprinkle the granulated garlic, salt, sugar, and black pepper over each pile of vegetables (use approximately half on each baking sheet). Gently toss the vegetables with your hands to evenly coat them in seasoning and then spread the vegetables across the baking sheets so that they are barely touching or overlapping (veg like room to roast). Put the baking sheets in a pre-heated 425° oven for 35-45 minutes (rotate half way) or until the vegetables are lightly golden on top and blistered and brown on the bottom. The onions should become very crispy.
When the vegetables are done roasting, remove the pans from the oven and immediately sprinkle the grated Parmesan cheese over top (use approximately half on each baking sheet). Let the warmth of the pans help to slowly melt the cheese around the vegetables. Then transfer everything to a large serving platter. Be sure to scrape any brown bits or stuck-on cheese onto the platter as well (these are the best part when paired with the buttery roasted potatoes or squash).