Place a frying pan over a medium high heat and add both the olive oil and butter. When the butter has melted add the salmon fillets and cook for about 2-3 minutes on each side. Remove from the pan and put to one side for now removing the skin.
1 tbsp unsalted butter, 1 tbsp olive oil
Add the asparagus to the same pan and cook for about 2 minutes if thin or 3 minutes if thicker.
1 bunch asparagus
Add the garlic while the asparagus is still in the pan and cook, stirring well for about 30 – 45 seconds.
4 cloves garlic
Add the cream, lemon juice and zest (See note 2) and the grated parmesan and stir to combine.
1 large lemon, ¾ cup heavy cream, 2 oz parmesan
Gently break the salmon into chunks and return them to the pan and stir in/toss to coat.
The tagliatelle should be cooked by now so drain well.
Add the al dente pasta to the salmon and saucepan and toss everything together. Leave to cook for a couple of minutes more until the asparagus and salmon are perfectly cooked.
Serve immediately with a further grating of parmesan and a sprinkle of rocket/arugula leaves.
1 oz arugula
Notes
Note 1: I try to select the thinner asparagus stems as they become love and soft.Note 2: The lemon zest should be added slowly and tasted to make sure it doesn't overpower the dish. Start by adding a 1/4 of the zest, stir and then taste. If you prefer more then add a little more and repeat.Note 3: The easiest method is to hold one between the thumb and forefinger of each hand with one hand at the base and the other about half way up. Slowly bend the asparagus and it will naturally snap at the spot between the hard and delicate soft section. Use that spear to cut the rest.