Preheat oven to 425°F (220°C). Line a baking sheet with parchment paper.
Place asparagus and carrot sticks on the baking sheet in a single layer.
Drizzle the vegetables with olive oil and sprinkle with garlic, Italian seasoning, paprika, salt, and black pepper. Toss well until evenly coated.
Roast for 20–25 minutes, turning halfway through, until the carrots are tender and the asparagus is lightly crisp and roasted around the edges.
Sprinkle parmesan cheese over the vegetables during the last 2–3 minutes of roasting if using.
Garnish with fresh parsley and serve with lemon wedges for extra brightness.
