Bring a large pot of salted water to a boil. Add the linguine, and cook until it’s al dente. Reserve ¼ cup of the pasta water, drain the noodles, and set aside.

While the pasta cooks, make the lemon sauce and cook the asparagus.

In a large saucepan, add 6 tablespoons of olive oil, unsalted butter, lemon juice, and lemon zest. 

Cook over low heat until the butter melts. Whisk briefly to combine, then remove from heat.

Heat a medium skillet over low to medium heat. Add the remaining 2 tablespoons of olive oil, asparagus, and a sprinkle of salt and pepper to the hot pan. 

Cook for 3 to 5 minutes or until the asparagus is almost cooked to the desired consistency, then add the garlic. Cook for another 30 seconds, and remove from heat.

Add the pasta and cooked asparagus to the lemon sauce. Toss to combine, then add the cheese and a splash or two of the pasta water to loosen the sauce. Add more pasta water if needed.

Taste, and season with salt and pepper if desired.