1. Combine mint leaves, parsley leaves, 1/4 cup pistachios, olive oil, kosher salt, ground black pepper, and garlic in a mini food processor; pulse mixture until coarsely chopped.
2. Cook fettuccine according to the package directions, omitting salt and fat. Drain fettuccine over a bowl, reserving 1/4 cup of the cooking liquid. Combine pesto mixture and reserved cooking liquid in a large bowl, stirring with a whisk. Add pasta to bowl; toss well to coat. Gently fold in cherry tomatoes. Coarsely chop remaining 4 teaspoons pistachios. Top pasta evenly with pecorino Romano cheese and chopped pistachios.