Pulse all sauce ingredients together until smooth. Set aside.
Cook spaghetti according to package directions. Drain and set aside.
Heat the cherry tomatoes in a large skillet over medium high heat with a very quick drizzle of olive oil. Gently shake the pan to get them moving (you might want to grab a lid for this - they really start to spatter when the juices hit the hot oil). Continue cooking until tomatoes are roasty-looking and the skins are split or loosened. Remove from heat and set aside.
Add the zucchini to the same pan and toss for 1-2 minutes, until tender-crisp. Add the spaghetti and the avocado sauce. Toss until combined. Season with salt and pepper, top with reserved tomatoes and Parmesan if you like that sort of thing. Serve immediately.