Bring a large pot of well-salted water to a rolling boil. Cook the pasta according to package directions until al dente. Just before draining, carefully reserve 1 1/2 cups of the starchy pasta water. Drain the pasta and set aside.

While the pasta cooks, heat 2 tablespoons of olive oil in a large skillet or Dutch oven over medium heat. Add the sliced shallot and a pinch of salt. Cook, stirring often, until soft and translucent, about 3-4 minutes.

Increase the heat to medium-high. Add the asparagus pieces to the skillet. Cook undisturbed for 1 minute, then stir and cook for another 2-3 minutes until bright green and tender-crisp.

Add the fresh peas (if using) and cook for 1 more minute. (If using frozen peas, wait for the next step).

Reduce the heat to medium. Pour in the heavy cream (if using), lemon zest, and 1/2 cup of the reserved pasta water. Bring to a simmer. If using frozen peas, add them now. Let the sauce simmer for 1 minute to reduce slightly and warm the peas.

Add the drained pasta to the skillet with the vegetables and sauce. Using tongs, toss everything vigorously. Add more pasta water, a splash at a time, until a loose, glossy sauce coats every strand.

Remove the skillet from the heat. Add the cold butter, lemon juice, and half of the grated Parmigiano-Reggiano. Toss continuously until the butter is completely melted and emulsified into a velvety sauce.

Taste and season generously with salt and black pepper. Fold in most of the fresh herbs. Divide among bowls and top with the remaining cheese, herbs, and a final drizzle of the remaining 1 tablespoon of olive oil.