For the pesto
- Toast the walnuts over medium-low heat in a large sauté pan for 7-8 minutes, stirring frequently, until lightly toasted. Transfer to a plate and wipe the pan clean.
- Remove parsley leaves from the stems and add them to the bowl of a food processor. Discard stems. Pulse until the parsley is well chopped. Add the toasted walnuts, lemon zest, and salt and process until the mixture is uniform, scraping down the sides as necessary. With the machine running, slowly add the lemon juice and 3 tablespoons of olive oil. Set pesto aside.
For the shrimp and zoodles
- Pat the shrimp dry with a paper towel and remove tails if desired.
- Heat the large sauté pan over medium heat. Once hot, add the remaining tablespoon of olive oil and the garlic. Sauté, stirring frequently, until fragrant, about 30 seconds. Add the shrimp, salt and pepper to taste, and cook, flipping shrimp about halfway through cooking time, until the shrimp are pink and curled, 4-6 minutes total.
- Add the zoodles and cook for one minute, stirring frequently. Add the pesto and stir to combine. Add the tomatoes and give the mixture one more stir to fully coat the veggies and shrimp with the pesto. Serve immediately.
Note: If your pan is not large enough to hold all of the shrimp and zoodles at the same time, remove the cooked shrimp from the pan before adding the zoodles. Cook the zoodles for two minutes, stirring frequently. Combine the cooked zoodles, reserved shrimp, pesto, and tomatoes in a large serving bowl and stir to evenly coat the veggies and shrimp with the pesto.