Bring a pot of SALTED water to boil in a pasta pot.
Add in your spaghetti to start cooking. You want to time this so that the pasta is nearing al dente by the time you add the butter to the sauté pan (three steps ahead of now).
After spaghetti has been cooking for a few minutes, carefully take out a cup or so of the pasta cooking water and set it aside. You want to make sure you retrieve the water at the point where it has some of the starch from the pasta in it, so don't take it too soon.
Bring the same pan that you used for the zucchini back to medium-low heat. Add in the olive oil. Once the oil is hot, add in the garlic and sauté until fragrant, about 1 minute. Be careful not to let the garlic brown!
Then, add the white wine to the pan and stir it around, scraping any bits you can off the bottom of the pan. Reduce heat to low, and add in the butter. Stir until all of the butter is melted. (You can add more salt here if you want, but by using the salted butter and the salted pasta water, you may be fine with the salt level as is.)
At this point, the pasta should be slightly undercooked but nearing al dente. You want the pasta to be at a firmer texture than you'd eat it at because you will continue cooking in the sauce.
Using tongs, take the pasta directly from the water and place it in the sauté pan (which should still be on low heat). Once all of the pasta is in, add in about 1/4 cup of the pasta water, then toss the pasta in the sauce until it's all coated. (You can add more pasta water increments of 1-2 tbsp if things get dry.) Continue to cook the pasta in the sauce until it's al dente.