Bring a pot of salted water to a boil. Add 4 oz (115 g) of dry spaghetti and cook according to package instructions until al dente (usually 8-10 minutes). Drain and set aside.
In a blender or food processor, combine the basil, arugula, garlic, olive oil, Greek yogurt, water, Parmesan cheese, salt, and pepper. Blend until smooth, scraping down the sides as needed. If the sauce is too thick, add 1-2 tsp more water. Taste and adjust seasoning.
Spiralize the zucchinis using a spiralizer or julienne peeler.
Heat 1 tsp olive oil in a large skillet over medium heat. Add the zucchini noodles and sauté for 2 minutes, tossing gently. Remove from heat immediately to prevent them from becoming mushy.
In a large pot, toss the cooked spaghetti, sautéed zucchini noodles, Parmesan cheese, and fresh arugula. Pour the pesto sauce over the mixture and gently combine until everything is evenly coated.
Divide into bowls and garnish with extra basil or a sprinkle of Parmesan cheese (optional). Best enjoyed immediately.