Cook pasta according to package directions. DO NOT DRAIN WATER. With a slotted spoon, remove pasta and transfer to bowl and set aside. Add broccoli florets to pasta water and bring to a boil. Reduce heat and simmer for 3-4 minutes until broccoli is just tender. Drain and set broccoli aside.
In a large, deep skillet over medium-high heat olive oil. Add garlic and onion and cook until onions are translucent.
Add boiled broccoli and sauté for 1 minute. Then add carrots, zucchini, squash, red bell pepper, salt and pepper — sauté until just tender, about 3-4 minutes.
Add cherry tomatoes and peas and cook for another 1-2 minutes.
Pour in white wine, add lemon zest and lemon juice. Let simmer for 3-4 minutes.
Add pasta to the veggies and combine thoroughly. Pour into a large serving bowl.
Add Parmesan cheese and parsley to the veggies and pasta, stirring gently. Add additional salt and pepper to taste. Serve warm or refrigerate and serve cold.