Grate the Pecorino Romano cheese on the small edge of a box grater, and set it aside. Spiralize the zucchini and set it aside. You will need a spiralizer to make the noodles. Otherwise, you can make 3 cuts lengthwise with a sharp knife into the zucchini and use a vegetable peeler along the zucchini to make ribbon noodles.
Add the butter to a pan set over medium heat. Add the cracked black pepper and za’atar and stir to combine. Simmer for a couple of minutes until the butter begins to foam.
Add the zoodles to the pan. Use tongs to coat the zoodles in the butter-pepper sauce. Cook for 1 minute, enough to soften slightly but retain a bit of bite. Add the Pecorino Romano cheese to the pan, coating the zoodles.
Immediately transfer the zoodles to a dish. Drizzle with extra virgin olive oil. Serve.