Roasting the carrots add another layer of natural sweetness but if you're looking to save time -- and some calories -- steam your carrots.
Preheat oven to 400 degrees. Drizzle carrots with oil, and season with salt. Roast until soft and charred, about 45 minutes. Toss parsley with vinegar, olive oil, and cheese. Mash carrots, and spread onto toasts; top with parsley mixture.