Place the noodles in a large bowl, cover with boiling water and soak for 2 minutes.
Scoop out ½ cup (120 ml) of the noodle soaking water, then drain the noodles and run under cold water, breaking the noodles up with your hands.
Heat a large skillet over medium-high heat.
Add 1–2 tablespoons of olive oil, along with the zucchini and a pinch of sea salt, and stir-fry for 1–2 minutes, until softened.
Add the noodles to the pan, along with the butter, za’atar, another pinch of sea salt, and a few turns of black pepper and stir for 1 minute, until fragrant.
Add about ¼ cup of the noodle soaking water, just enough to loosen the noodles.
Cook for 1 minute, then turn off the heat, add half the cheese or nutritional yeast and season well with sea salt.
Toss everything together until the cheese melts, adding a bit more of the reserved soaking water if the noodles seem dry.
Transfer to serving plates and top with the remaining cheese or nutritional yeast, another turn of black pepper, more za’atar, and a few mint leaves.
Serve immediately.