Preheat oven to 400 and line a baking sheet with parchment paper.
Place potatoes in a mixing bowl with garlic and 2 tablespoons olive oil. Mix well to evenly coat.
Break the ends off of the fresh asparagus and discard. Place asparagus on baking sheet and drizzle with remaining 2 tablespoons olive oil. Use your hands to mix the asparagus and coat evenly. Spread asparagus in a single layer on the baking sheet. Add potatoes to baking sheet, keeping in a single layer.
Sprinkle with salt and pepper.
Roast vegetables for 20 minutes. Check the doneness of the potatoes and if necessary continue to roast for 2-5 minutes or until tender. Remove from oven and serve with shredded cheese.