Boil a large pot of water and add a generous pinch of salt. When boiling, stir in the pasta and cook just to al dente, according to package directions. Before draining, use a liquid measuring up to scoop out about 1 cup of the pasta water. Drain the rest of the water and set pasta aside.

While waiting for the water to boil and pasta to cook, start the veggies. Fill a medium saucepan with about one inch of water and place a steamer basket on top. Bring the water to a boil, then add carrots to the steamer basket. Cover and cook for 1-2 minutes, then add the broccoli florets and cover again. Add the peas after another 2-3 minutes, then cover again and continue to cook until the veggies are bright in color and tender-crisp. At that point, remove them from the heat and set aside.

When the veggies are almost done, begin the sauce. Melt butter in a large skillet over medium heat. Add minced garlic and cook for 30-60 seconds, just until fragrant. Add the steamed veggies and toss to coat, then add the drained pasta and toss again.

Add lemon juice, Parmesan, and about half of the reserved pasta water. Stir until the cheese smooths out into a thin sauce, adding more pasta water if needed.