Peel the carrots and pierce with the parisienne scoop at a slight angle (this may require a little effort because carrots are so fibrous), then twist the scoop back and forth until the small ball is formed and slips from the carrot. Continue this process with the carrots, zucchini, and yellow squash until you have 1 cup each.

Bring a small saucepan of water to a boil. Add the carrot balls and cook for 1 minute, or until the water returns to a boil. Remove and rinse under cold water to stop the cooking. Set aside. In a large 1 1/2-gallon pot, bring 1 gallon of water to a boil and season with salt. Place the penne pasta in the pot and return to a boil. While the pasta is cooking, heat a large 12 to 14-inch saute pan over medium-high heat. When hot, add the olive oil and heat for 30 seconds. Add the onions and cook for 3 to 4 minutes, until translucent and slightly browned around the edges, stirring frequently. Add the garlic and cook for 30 seconds. Add the zucchini and squash and continue sauteing the vegetables for an additional 3 minutes, stirring occasionally. Add the carrots and cook for 1 minute. Season with the salt, pepper, thyme, and parsley and toss to evenly combine.

When the pasta is al dente, drain in a large colander and transfer the cooked penne to the saute pan along with the cooked veggies. Add 1/4 cup of the Parmigiano-Reggiano and toss to blend. Taste and adjust seasoning if necessary. To serve, divide the pasta among 4 pasta bowls and sprinkle with some of the remaining freshly grated Parmiggiano-Reggiano. Serve immediately.