Heat the olive oil in a large skillet or wide pot over medium heat until shimmering.
Add the sliced mushrooms, zucchini, minced garlic, and dried thyme to the skillet and cook, stirring often, for about 5 minutes until the vegetables soften and the mushrooms release their juices.
Add the uncooked whole-wheat spaghetti, water, kosher salt, and ground black pepper to the pan; press the pasta down so it is mostly submerged in the liquid.
Bring to a boil, then reduce heat to a simmer and cook, stirring occasionally, for about 10 minutes or until the pasta is tender and the water is mostly absorbed.
Remove from heat, stir in the grated Parmesan until melted and evenly distributed, then sprinkle with chopped parsley.
Serve immediately.