Preheat oven to 450 degrees. Prepare a large baking sheet with parchment paper, a silicone baking mat, or foil (if using foil, spray it very well with cooking spray).
In a medium bowl, toss carrots with 1 ½ tablespoons of oil. Pour onto one end of the baking sheet in a single layer, leaving space for the asparagus. Sprinkle carrots with ½ teaspoon of garlic salt and roast in the oven for 15-20 minutes [for softer, more caramelized carrots, cook for the full 20 minutes].
Wash asparagus and trim about 1 ½ inches off of the thicker end of the stalks, discarding the trimmings. Grate the parmesan cheese.
After carrots have roasted for 15-20 minutes, remove from the oven and turn oven down to 400 degrees. Add the asparagus to the hot baking sheet, laying it out next to the carrots, in a single layer. Drizzle asparagus with the remaining 1 tablespoon of oil and ½ teaspoon of garlic salt. Return to the oven and cook carrots and asparagus together for 15 minutes.
Remove vegetables from the oven and sprinkle with freshly grated parmesan cheese. Return to the oven and cook for another 3-5 minutes, or until parmesan is melted and starting to slightly brown. Remove from oven, sprinkling with any other seasonings as desired and serve immediately.