Cook the Pasta: Bring a large pot of salted water to a boil and cook the tagliatelle according to the package instructions until al dente. Reserve 1/2 cup of pasta water before draining.
- Cook the Asparagus: While the pasta is cooking, heat the olive oil in a large skillet over medium heat. Add the asparagus pieces and sauté for 3-4 minutes until tender, but still crisp. Add a pinch of salt and pepper to taste. Remove the asparagus from the skillet and set aside.
- Prepare the Sauce: In the same skillet, add the minced garlic and cook for 30 seconds, until fragrant. Add the vegetable or chicken broth, lemon zest, and lemon juice, stirring to combine. Let the sauce simmer for 1-2 minutes, allowing it to reduce slightly.
- Combine Pasta and Sauce: Add the cooked tagliatelle to the skillet, along with the cooked asparagus. Toss everything together, adding reserved pasta water as needed to help the sauce coat the pasta. Continue to toss until everything is well-mixed and heated through.
- Finish the Dish: Stir in the grated Parmesan cheese, and season with more salt and pepper to taste. If desired, add a bit more pasta water for a silkier sauce.
- Serve: Divide the pasta into bowls and garnish with extra Parmesan cheese and fresh parsley. Serve immediately.