Bring a pot of salted water to boil. Cook the spaghetti until al dente. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Add onion and garlic and cook until softened.
Add bell peppers, zucchini, yellow squash, and broccoli. Cook until vegetables are tender-crisp.
Stir in cherry tomatoes and cook for another 2 minutes.
Toss the cooked pasta into the skillet with the vegetables. Season with salt and pepper.
Remove from heat and sprinkle with Parmesan cheese. Garnish with basil before serving.