In a large pot, melt butter over medium heat. Add shallot and sauté for 3 minutes. Add garlic and sauté for 30 more seconds until fragrant.
Add pasta to the pot along with chicken broth, salt, and pepper. Bring to a boil and reduce the heat to medium/low. Cook for 8 minutes, stirring every 1-2 minutes. Add asparagus and continue to cook until pasta is al dente, about 3 to 4 minutes.
Turn off the heat. Stir in pesto, lemon zest, and lemon juice. Transfer the pasta to a serving plate, and top with dollops of cheese. Cut into a few pieces of the cheese and drizzle the cheese with olive oil. Serve immediately.
