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champagneraccoon
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Arrange a rack in the middle of the oven and heat the oven to 425°F. Meanwhile, line a rimmed baking sheet with parchment paper. Finely grate 3 ounces Parmesan cheese on the smallest holes of a box grater (about ¾ packed cup), or measure out 1 cup store-bought grated. Transfer to the baking sheet and spread into an even layer.
Peel 1 pound medium carrots and trim the ends. Halve crosswise, then halve or quarter each piece lengthwise so they are all about the same size. Place in a large bowl. Pick the leaves from 1 fresh rosemary sprig and finely chop until you have 1 ½ teaspoons, or measure out ¾ teaspoon dried rosemary. Add to the bowl.
Add 1 tablespoon olive oil, ½ teaspoon dried oregano, ¼ teaspoon kosher salt, and ⅛ teaspoon black pepper. Toss until the carrots are evenly coated. Arrange the carrots cut-side down in a single layer on the cheese, spacing them evenly apart.
Roast until most of the cheese is dark golden-brown and the carrots are tender, rotating the baking sheet as needed, 15 to 20 minutes total. Let cool for 2 to 3 minutes. Garnish with freshly chopped parsley leaves if desired.