Add the kale, basil, Parmesan, broth, walnuts, salt, matcha, and garlic to a food processor and pulse until the greens are finely chopped. Scrape down the sides as needed to ensure everything is incorporated and well blended.
Then drizzle in the olive oil while you continue to pulse until everything is evenly blended. Season with additional salt, ground black pepper, and garlic to taste. (Mix in 1 to 2 tablespoons extra broth if a thinner texture is desired.)
Toss the kale pesto sauce with cooked pasta and tomatoes.
Nutrition information is calculated using a leading industry software. That being said, brands can vary, and there may be slight fluctuations in the numbers.