Trim 1 medium bunch asparagus and cut crosswise into 1-inch pieces. Finely grate the zest of 1 medium lemon (about 2 teaspoons). Juice the lemon until you have 2 tablespoons. Pat 1 pound boneless, skinless chicken breasts dry with paper towels and cut into 1/2-inch-wide strips. Season the chicken all over with 1/2 teaspoon of the kosher salt and 1/4 teaspoon black pepper.
Heat 1 tablespoon of the olive oil in a Dutch oven or large pot over medium-high heat until shimmering. Add the chicken in a single layer and cook, flipping occasionally, until cooked through and browned all over, 5 to 8 minutes total. Transfer the chicken to a plate.
Add 3 cups water, 1 cup heavy cream, the remaining 2 tablespoons olive oil, remaining 1 3/4 teaspoons kosher salt, and 12 ounces short dried pasta to the Dutch oven, and stir to combine. Bring to a boil over high heat. Continue to boil, stirring occasionally with a wooden spoon to prevent the pasta from sticking to the bottom of the pot, until the pasta is 2 minutes less than al dente, 5 to 9 minutes depending on the pasta shape. Meanwhile, finely grate 1 ounce Parmesan cheese (about 1/2 cup lightly packed) if needed, or measure out 1/3 cup store-bought.
Add the asparagus to the pasta and stir to combine. Cook until the asparagus is crisp-tender and pasta is al dente, 1 to 2 minutes.
Remove the pot from the heat. Return the chicken and any accumulated juices on the plate to the pot and add the lemon zest, juice, and Parmesan cheese. Stir until well-combined and the pasta is coated with the cheese. Taste and season with more kosher salt as needed.
Recipe Notes