Bring a large pot of water to a boil over high heat. Drop in spaghetti and a few big pinches of kosher salt, stirring to combine. Once the water comes back to a boil, reduce heat to medium-low and cook spaghetti according to the package instructions. Before you drain the spaghetti, scoop out a cup of starching cooking water, and set aside.
Meanwhile, warm butter and garlic in a large skillet over medium-low heat. Cook until the garlic is soft and fragrant (but not brown, 3 - 5 minutes). Add the spiralized zucchini, a big pinch of salt and several turns of black pepper, and toss in the garlic butter. Cook just until the zucchini starts to soften (about 2 minutes).
Drop heat to low and add drained spaghetti, chopped herbs, Parmesan cheese and a splash of starchy cooking liquid to the skillet, tossing to combine. Season to taste with salt and black pepper. If the pasta is looking a little dry, add more starchy cooking liquid. You want to add just enough to make the butter sauce creamy, but not so much that it starts pooling in the bottom of the pan. Take the pan off the heat once you're done making adjustments.