Cook the pasta according to package instructions in a large pot of salted boiling water. Drain and set aside, reserving 1/2 cup of pasta water.
In a large skillet, heat the olive oil over medium heat. Add the diced onion and sauté for about 3 minutes until translucent.
Stir in the minced garlic and cook for an additional 1 minute until fragrant.
Add the zucchini, yellow squash, and bell pepper to the skillet. Sauté for about 5 minutes until the vegetables are tender.
Add the broccoli florets and cherry tomatoes, cooking for another 3-4 minutes until the broccoli is bright green and the tomatoes start to soften.
Sprinkle in the dried oregano, dried basil, salt, and pepper. Stir to combine.
Add the cooked pasta to the skillet along with the reserved pasta water. Toss everything together until well mixed and heated through.
Remove from heat and stir in the grated Parmesan cheese until melted and evenly distributed.
Serve warm, garnished with fresh basil leaves if desired.