Place carrots and shallots in a pan; cover with water. Bring to boil; cook until tender, 7 minutes. Drain.
Preheat oven to 425°F. In a large bowl toss carrots, shallots, fennel and garlic cloves with 2 Tbsp. olive oil, 1 Tbsp. chopped garlic, 1 Tbsp. tarragon, salt and pepper. Spread in a single layer on a baking sheet. Roast for 15 minutes, stirring once.
Toss remaining vegetables with remaining olive oil and garlic, 1 Tbsp. tarragon, salt and pepper. Place on a baking sheet in a single layer and roast on separate oven rack for 25 minutes, stirring occasionally. Toss all vegetables together, sprinkle with 1 Tbsp. tarragon and serve.