Bring a large pot of salted boiling water, drop in the linguine and cook until al dente.
While the pasta is cooking, prepare your ingredients. Snap off and discard the toughest part of the asparagus at the bottom. Cut the tips of the asparagus and set aside for later. Dice the stems into 2cm thick pieces and drop these into the pasta water too.
In a large frying pan on a medium-high heat, add ⅔ of the butter, along with a good drizzle of olive oil. Use the mint like a brush and stir the butter and oil mixture together then drop the mint into the pan. Cook the butter until brown and deglaze with a good ladle of the pasta water to stop it from burning.
Add the asparagus tips to the pan and cook then for 2 minutes. You want them to still be crunchy.
When the pasta is ready, discard the mint from the pan and transfer the linguine directly from the pasta water to the sauce. Give it a good stir.
Using a slotted spoon, collect all the chopped asparagus stems from the pasta water and add this to the sauce as well.
Turn the heat off and add a good amount of freshly ground black pepper, a little of the lemon zest, the lemon juice, the rest of the butter and a generous amount of grated cheese. Give it a good stir all together to combine, until you create a really nice creamy sauce. If it's too thick or too dry, use some more of the pasta water to loosen the sauce.
Serve up and top with a final sprinkle of grated cheese and enjoy.
