Bring a large pot of heavily salted water to a boil. Cook the spaghetti according to the package directions until just al dente. Before you drain it, scoop out about 1/2 cup of the starchy pasta water and set it aside. Drain the pasta and set it aside.

While the pasta cooks, place a large skillet over medium-high heat and add the butter. Let it melt and continue cooking, swirling the pan occasionally, for about 3 to 4 minutes. You will see the foam settle and then the butter will turn a golden amber color and start to smell nutty, like toasted hazelnuts. That is your signal it is ready. Do not walk away during this step because it can go from brown to burned quickly.

Add the zucchini slices to the brown butter in a single layer. Season with 1 teaspoon of salt and the black pepper. Cook over medium-high heat, without stirring too much, for about 4 to 5 minutes. You want the edges to turn golden and the pieces to be tender but not mushy. Stir once or twice so they cook evenly.

Push the zucchini to one side of the pan and add the minced garlic to the open space. Cook the garlic in the butter for about 60 seconds, stirring it constantly, until it is fragrant and just turning golden. Stir everything together and reduce the heat to medium-low.

Add the drained spaghetti directly to the skillet. Pour in about 1/4 cup of the reserved pasta water and toss everything together with tongs. The starchy water will help the butter cling to the noodles and form a light sauce.

Remove the pan from the heat and sprinkle in the Parmesan cheese. Toss again, adding a splash more pasta water if the pasta looks dry or clumped. Taste and adjust salt. Add red pepper flakes if you like a little heat. Serve immediately with extra Parmesan at the table.