Combine peas, cashews, lemon zest, lemon juice, garlic, salt and pepper in a food processor. Pulse until finely chopped. Add basil and spinach; pulse until finely chopped, pausing to scrape down the sides. With the motor running, drizzle in ¼ cup oil and water; process until smooth.
Heat the remaining 1 tablespoon oil in a large nonstick skillet over medium heat. Add gnocchi and cook until starting to crisp and lightly brown, about 3 minutes. Stir and continue cooking until the gnocchi are golden on all sides, 3 to 5 minutes more. Add the pesto and cook, stirring, until hot, about 1 minute. Serve the gnocchi with burrata and pea shoots, if desired.
