Process thawed frozen sweet peas, Parmigiano-Reggiano cheese, lemon zest, fresh lemon juice, extra-virgin olive oil, chopped fresh mint, garlic clove, kosher salt, and black pepper in a food processor until smooth, about 1 minute, adding water, 1 Tbsp. at a time, and processing until smooth. Transfer to a bowl. Sprinkle with chopped mint and lemon zest.