Bring a large pot of salted water to a boil. Add asparagus and green beans; cook 4 minutes. Add peppers and cook 1 more minute. Scoop out vegetables with a large slotted spoon and place in a colander. Rinse under cold water.
Add pasta to boiling water and cook following package directions, about 9 minutes. Drain; return to pot.
While pasta is cooking, place half-and-half, chicken broth, salt, pepper and nutmeg in a small saucepan. Bring to a simmer over medium heat.
Heat a large nonstick skillet over medium-high heat. Add olive oil and garlic and cook 30 seconds. Add cooked veggies and tomatoes. Cook, stirring a few times, about 1 minute, 30 seconds. Spoon into pasta pot. Stir grated cheese into the half- and-half mixture. Add to pasta and gently stir in parsley until all ingredients are combined. Allow to stand for 5 minutes. Shave Parmesan on top, if desired.