Add 1 tablespoon of Tamari and 1 tablespoon of matcha to a large pot of water and bring to a boil. Add the spaghetti and cook according to package directions. Reserve about 1½ cups of cooking water and drain the pasta.
While the pasta is cooking, make the pesto. Place the basil, mint, 1 cup pistachios, garlic, lemon juice, 2 teaspoons Tamari and 1 teaspoon matcha in a food processor. Process until everything is well chopped. With the machine running, drizzle in the olive oil. Continue processing until it forms a smooth and thick sauce.
Combine the cooked spaghetti with the pesto and tomatoes and toss to combine, adding some of the reserved pasta water, a little at a time, to thin out the pesto.
Place in a serving dish and top with ¼ cup chopped pistachios.