Begin by bringing a large pot of generously salted water to a boil. Add the fresh fettuccine and cook according to the package instructions, ensuring it is al dente—tender, but with a slight firmness. After draining, reserve 1/2 cup of the pasta water and toss the pasta with a splash of olive oil to prevent sticking.

While the pasta is cooking, prepare the vegetables. Slice the shiitake mushrooms into thin 1/4-inch strips and cut the woody ends off the asparagus, slicing it into 2-inch pieces. Heat a large skillet over medium heat and melt 2 tablespoons of butter. Raise the heat to medium-high, then add the mushrooms in a single layer. Allow them to brown undisturbed for 1 to 2 minutes, then stir and cook until golden brown, about 2 more minutes. Add the asparagus along with an additional tablespoon of butter and 1/2 teaspoon of salt. Continue to cook, stirring occasionally, until the asparagus becomes tender and the mushrooms are fully browned, 2 to 4 minutes. Once done, transfer the vegetables to the colander with the pasta.

Lower the heat to medium and add the remaining 5 tablespoons of butter to the skillet. Once mostly melted, whisk in the heavy cream and bring the mixture to a simmer. Stir in the peas and cook for 2 minutes before turning off the heat.

Gradually whisk the freshly grated Parmigiano-Reggiano into the sauce. Add the sautéed vegetables, cooked fettuccine, chopped chives, and lemon zest. Toss thoroughly to combine. Season the dish with salt and freshly ground black pepper to taste. If the sauce thickens too much as it cools, thin it out by adding the reserved pasta water, one tablespoon at a time, until the desired consistency is reached. Serve immediately in pre-warmed bowls for optimal presentation.