Spiralize 3 zucchini. Square off the ends of the zucchini and place them in the spiralizer. Use a medium spiral blade.
Place the zucchini in a bowl or colander and toss with 1 teaspoon of sea salt. Set aside (set over a drain if using a colander) and allow the zucchini to weep (release its water.) After about 30 minutes, drain any water that has been released from the zucchini, then wrap the zoodles in a clean dishcloth and gently squeeze as much of the remaining water from them as you can.
Prepare the remaining vegetables by dicing, spiralizing, or slicing.
Melt butter in a large skillet over medium heat.
Add onions and mushrooms to the skillet and saute for about 2 minutes, until softened.
Add the minced garlic to the pan and cook 1 minute longer.
Add the bell pepper, broccoli, and carrots to the pan and cook, tossing gently, for 2 minutes longer, until the vegetables have just begun to soften.
Add in the zoodles, chiffonade basil, and cherry tomatoes. Cook 3-4 minutes longer, until the zoodles begin to soften.
Add cream, then parmesan cheese, and additional salt and pepper to taste. Cook and stir for 1 additional minute, until the cheese has melted and the cream sauce is coating the zoodles and other vegetables.
Serve immediately.
Notes
Store in an airtight container in the refrigerator for up to 3 days.We used a Kitchen-Aid spiralizer attachment for automatic spirals. There are other brands of spiralizers that are manual, if you do not have a Kitchen-Aid. (I chose the kitchen-aid attachment because it was not much more expensive than a plastic manual spiralizer.)Weeping the zucchini helps to keep excess liquid out of the pasta primavera, allowing the dish to cook up more quickly and prevent the vegetables from boiling and losing flavor in the excess water.We loved ½ cup of heavy cream for a nice creamy sauce, but you can certainly substitute milk and/or use less to lighten the meal further.You can serve with additional parmesan cheese and fresh basil leaves.