Prepare all vegetables: slice 1 cup zucchini, trim and cut 1/2 cup asparagus into thirds, dice 1/2 cup bell pepper, and halve 2/3 cup tomatoes if large. Measure out 12 ounces of pasta.

Bring a large pot of salted water to a rolling boil. Add the pasta and cook according to package directions until al dente (about 8-10 minutes). Drain the pasta, reserving 1/2 cup of the pasta water, and set aside. Do not rinse the pasta.

While the pasta cooks, heat a large skillet over medium heat. Melt the 3 tablespoons of butter. Add the 1 teaspoon of minced garlic and cook for 1 minute until fragrant. Add the sliced zucchini, asparagus, and diced bell pepper, and cook for another 1 minute, maintaining medium heat to keep the vegetables tender-crisp.

Pour in 1 cup of broth and bring the mixture to a brief simmer over medium-high heat. Cook for 2-3 minutes until the vegetables soften slightly. Stir in the 1 cup heavy whipping cream, 1/2 cup petite peas, 1/2 cup snow peas, and 2/3 cup tomatoes. Reduce heat to medium-low and simmer gently for 2-3 minutes (around 180-200°F).

In a small bowl, mix the 1 1/2 tablespoons of cornstarch with 1 tablespoon of broth or water to create a slurry. Whisk this slurry into the simmering sauce in the pan and cook for about 1 minute until the sauce thickens. Remove the pan from the heat and stir in the 1/2 cup of shredded Parmesan cheese.

Add the cooked pasta to the skillet with the sauce and toss to combine thoroughly. If the sauce is too thick, add a little of the reserved pasta water, one tablespoon at a time, until it reaches your desired consistency. Season the dish generously with salt and pepper to taste.

Taste the pasta and adjust the seasoning as needed. Serve immediately in bowls, garnished with extra Parmesan cheese or fresh herbs if desired. This dish pairs wonderfully with a fresh salad.