Preheat oven to 425. Toss the cut carrots on a rimmed baking sheet with olive oil and season with salt and pepper. Roast until tender, about 20-25 minutes. Drizzle with maple syrup and roast for an additional 5 minutes.
Meanwhile, combine the cranberries and orange juice in a small saucepan and bring to a simmer. Remove from heat and allow to sit for 10 minutes to plump up the dried fruit. Grate the garlic into the vinegar in a small bowl.
Toss the arugula in a large bowl and top with the roasted carrots, goat cheese, chopped walnuts, and rehydrated cranberries, including any remaining juice. Add the vinegar dressing and toss well. Season with salt and pepper and eat right away.