Preheat oven to 425°F (220°C) with a rack in the middle. Line a rimmed baking sheet with parchment paper for easy cleanup.

In a large bowl, combine zucchini, yellow squash, bell pepper, and red onion. Drizzle with 1 tablespoon olive oil, sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper. Toss to coat evenly.

Spread vegetables in a single layer on the prepared baking sheet. Roast for 25-30 minutes, stirring halfway through, until tender and browned at the edges. The zucchini should be soft but not mushy, and the peppers should have charred spots.

While vegetables roast, bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente. Reserve 1/2 cup of pasta cooking water before draining. Drain pasta and set aside.

In a small bowl, whisk together balsamic vinegar, Dijon mustard, minced garlic, remaining 1/2 teaspoon salt, and remaining 1/4 teaspoon pepper. Slowly drizzle in the extra-virgin olive oil while whisking until emulsified.

In a large mixing bowl, combine the roasted vegetables, cooked pasta, and vinaigrette. Toss gently. Add 2-3 tablespoons of the reserved pasta water and toss again. The starch in the water helps the vinaigrette cling to every piece.

Fold in torn basil and Parmesan (if using). Taste and add more salt, pepper, or a splash of vinegar if needed. Serve warm or at room temperature.

Store leftovers in an airtight container in the refrigerator for up to 4 days. To revive, add a drizzle of olive oil or a splash of water and reheat gently.