Preheat the oven to 400°F (200°C). Line a large baking sheet with parchment paper; do not use foil so the cheese can crisp without sticking.
Spread 1½ cups of the shredded Parmesan in a tight rectangle on the parchment to form a base layer.
Peel the carrots and cut into 3 to 3½‑inch lengths. For thicker carrots, halve lengthwise and then crosswise so each piece is about ½ inch thick for even cooking.
In a large bowl, whisk together the olive oil, minced garlic, salt, onion powder, dried rosemary, and black pepper.
Add the prepared carrots to the bowl and toss until the pieces are fully coated with the seasoned oil.
Arrange the carrots cut side down on top of the Parmesan rectangle in a single layer, fitting them closely together so the bottoms caramelize. Sprinkle the remaining ½ cup Parmesan evenly over the tops of the carrots.
Bake for 30–35 minutes, or until carrots are tender and the cheese around the edges is golden and crisp. For softer carrots, bake an additional 5 minutes as desired.
Let the pan rest for a couple of minutes so the cheese crust firms, then transfer the carrots to a serving platter and garnish with chopped fresh parsley if desired.