Preheat oven to 375. Cut carrots into 2-inch long pieces, halving or quartering lengthwise if large. Place on a roasting sheet or cast iron skillet and toss with 1 tablespoon olive oil and a sprinkle of salt. Roast until soft, 30 minutes. Pour the juice and syrup into the roasting pan and stir, then cook 5-10 minutes more until caramelized. Scrape into a bowl and let cool completely.
For the dressing, combine all the ingredients in a bowl or sealable jar and whisk or shake until combined.
Place lettuce in your salad bowl with the cranberries, crumbled cheese and cooled carrots. Toss with dressing and serve. The salad can be composed, without the dressing, a few hours ahead of serving. Dress immediately before serving.