Trim and scrub the carrots. If the carrots are more than 1 inch in diameter, cut them in half lengthwise. Cut the carrots in large diagonal slices 1 inch wide × 2 inches long (they will shrink when they roast) and place in a medium bowl with 1/4 cup of olive oil, 1 teaspoon salt, and 1/2 teaspoon pepper. Toss well and transfer to two sheet pans. (If you use just one, they¿ll steam instead of roasting.) Roast for 20 minutes, tossing once, until the carrots are tender. Transfer all the carrots to one of the sheet pans, add the maple syrup, toss, and roast for 10 to 15 minutes, until the edges are caramelized. Watch them carefully! Toss with a metal spatula and set aside for 10 minutes.
Meanwhile, combine the cranberries and orange juice in a small saucepan, bring to a simmer, then set aside for 10 minutes.
In a small bowl, combine the vinegar, garlic, and 1/2 teaspoon salt. Whisk in 3 tablespoons of olive oil. Place the arugula in a large bowl and add the carrots, cranberries (with their liquid), goat cheese, almonds, and the vinaigrette. Toss with large spoons, sprinkle with salt, and serve at room temperature.