If you don't own a spiralizer, you can use a julienne peeler. Some grocery stores now sell premade zucchini noodles.
Spiralize zucchini into noodles (about 6 cups), and place in a large bowl. Add peas, onion, garlic, and parsley to bowl. Combine feta cheese, buttermilk, the lemon zest, and 1/4 tsp. pepper in a small bowl; stir until smooth. Just before serving, toss together zucchini noodle mixture and buttermilk dressing. Season with additional pepper and salt, if needed, and serve immediately.