Preheat oven to 400 degrees. Line a large rimmed baking sheet with aluminum foil. Place the carrots on the baking sheet, allowing space between each one. Add the garlic to the melted butter. Drizzle the carrots with the garlic butter mixture, turning to coat. Season the carrots with kosher salt. Roast for 20 minutes (15 for thinner carrots). Sprinkle the parmesan cheese evenly over the carrots and return to the oven to roast another 10 minutes, or until the cheese is golden brown and crispy and the carrots are tender-crisp. Sprinkle with parsley and serve.