Bring a large pot of well-salted water to a boil. With a pizza cutter or chef’s knife, cut the pasta sheets into rustic strips about 1/2 inch wide.
In a 10- to 11-inch straight-sided sauté pan, bring 2-1/2 cups water, the garlic, 1 tsp. salt, and 1/4 tsp. pepper to a simmer over high heat. Add the mixed vegetables and simmer briskly, adjusting the heat as necessary, until just crisp-tender, 3 to 4 minutes. With a slotted spoon, transfer to a large plate. If using peas, simmer them until barely tender, about 2 minutes, and transfer to the plate with the slotted spoon. (If using favas, skip this step.) Raise the heat to high and boil the liquid until reduced to 1 cup, 3 to 4 minutes.
Meanwhile, cook the pasta in the boiling water until barely al dente, 2 to 4 minutes. Drain.
Add the cooked pasta, vegetables, favas (if using), pea shoots or watercress, herbs, butter, and lemon zest to the broth. Toss over medium-high heat until the butter is melted, about 1 minute.
Season to taste with salt and pepper. Serve garnished with pea shoots or watercress, fresh herbs, and Parmigiano (if using).