If using fresh tomatoes, seed them by cutting in half along the equator and placing a strainer over a bowl. Seed the tomatoes into the strainer and rub the gelatinous seed pods against the strainer to extract flavorful juice.
Bring a large pot of water to a boil. Meanwhile, place the rice sticks in a large bowl, and cover with hot water. Let sit 20 minutes, until pliable. Drain and cut the noodles in half, into roughly 6- to 8-inch lengths, with kitchen scissors.
While the rice sticks are soaking, heat 1 tablespoon of the olive oil over medium heat in a wide, heavy skillet, and add the garlic. Cook, stirring, until fragrant, about 30 seconds, and add the zucchini. Cook, stirring, until the zucchini begins to soften and the skin becomes bright green, about three minutes. Add the tomatoes with juice and salt and pepper to taste. Cook, stirring often, for 6 to 10 minutes until the zucchini is tender and the tomatoes have begun to break down. Remove from the heat, taste and adjust seasonings, and set aside.
When the water comes to a boil, salt generously and add the rice sticks. Boil one minute and drain. Toss with the zucchini and tomato mixture, the remaining olive oil and the mint. Serve, passing the cheese for people to sprinkle on at the table. Serves four.