Preheat the oven to 425°F (220°C) to ensure caramelization and crisp edges.
Peel and cut the carrots into sticks or diagonal slices about ½ inch thick for even roasting.
Snap or trim the woody ends of the asparagus. Thinner spears will cook faster than thicker ones.
In a large bowl, toss asparagus and carrots with olive oil, minced garlic, salt, pepper, thyme, and optional lemon zest until evenly coated.
Spread the vegetables in a single layer on a baking sheet, leaving space between pieces to prevent steaming.
Roast for 20–25 minutes, tossing halfway through. Watch thinner asparagus tips to avoid burning.
Check doneness: carrots should be tender but slightly firm, asparagus crisp-tender.
Optional: Sprinkle with freshly grated Parmesan cheese immediately after roasting. Serve hot.