Bring a pot of salted water to a boil. Add the spaghetti and cook according to the package directions. Reserve about a cup of the cooking water, drain the pasta, and transfer it to a large serving bowl.
Meanwhile, heat the olive oil over medium-high heat.
Add the zucchini rounds and cook, stirring occasionally, until they are very tender and have reduced in size.
Transfer the cooked zucchini and any remaining cooking oil to the bowl of pasta. Season to taste with salt and pepper. Toss everything together to combine, adding a little of the reserved cooking water as necessary, then serve.
Smaller squash tend to be sweeter and less bitter than larger ones. Cut off and discard the ends, then slice into thin rounds with a chef's knife.
Before draining the pasta, use a coffee mug to reserve about a cup of the starchy cooking water. Adding a little in as you toss will help the zucchini and olive oil mixture stick to the spaghetti.
Zucchini has a high water content, so be sure to allow it to cook down before adding it to the cooked pasta. Don't be surprised when it reduces in volume as it cooks. It's not nearly as dramatic as with fresh spinach, but you will notice a difference. You can't really overcook the zucchini unless you forget about it and let it burn, so when in doubt, leave it on the stove a few minutes longer.
Storing:Leftover pasta can be covered and refrigerated for up to 3 days and reheated in the microwave. I do not recommend freezing it.