Cut carrots, zucchini and green onions into matchstick-size strips. Heat vegetable oil in large skillet over high heat. Add 2 tablespoons ginger and 1 1/2 teaspoons garlic; saute until fragrant, 30 seconds. Add carrots, zucchini, half of green onions and sesame oil; saute 2 minutes. Add remaining ginger and garlic; saute until vegetables are crisp-tender, about 1 minute longer. Using slotted spoon, transfer vegetables to bowl. Reduce heat to medium. Add 1 1/4 cups water, coconut milk, soy sauce and curry paste to same skillet. Stir until smooth. Simmer until sauce is reduced to 1 1/4 cups, about 6 minutes. Add sauteed vegetables and remaining onions. Meanwhile, cook somen in large pot of boiling salted water until just tender, about 2 minutes. Drain. Transfer to large bowl. Add vegetable mixture. Toss to coat. Sprinkle nuts and mint over.