In a blender, combine the basil, walnuts, Parmesan cheese, garlic, 1/2 teaspoon salt and 1/4 teaspoon pepper. Pulse until roughly chopped then with the blender running, stream in 1/2 cup olive oil and continue blending, scraping down the sides as needed, until the pesto is puréed. Set the pesto aside.

Add 1/2 tablespoon olive oil to a large sauté pan set over medium heat. Add the shrimp and a pinch of salt and pepper, and cook, stirring, until the shrimp are pink and cooked through. Using a slotted spoon, transfer the shrimp to a bowl.

Add the remaining 1/2 tablespoon olive oil to the sauté pan set over medium heat. Add the zucchini noodles and cook them, tossing frequently, until they’re softened slightly. Reduce the heat to low then add the shrimp and pesto to the pan and toss to combine. Serve immediately.