Bring water to a boil in a large Dutch oven over high heat. Add spaghetti; cook according to package directions. Reserve ½ cup cooking water; drain the spaghetti. Do not wipe the pot clean.
Meanwhile, process spinach, basil, oil, lemon juice, garlic and salt in a blender until smooth and bright green, 1 to 2 minutes.
Transfer the spinach mixture to the Dutch oven; add the cooked spaghetti and toss with tongs until well coated. Add the reserved cooking water, 2 tablespoons at a time as needed, to thin sauce.
Divide among 4 bowls. Top with 1 tablespoon each Parmigiano-Reggiano and walnuts; sprinkle evenly with pepper and lemon zest. Garnish with additional basil, if desired.
