Preheat a pan at medium-high heat.
Add the butter and olive oil (olive oil prevents the butter from burning) and use them to sear the salmon on both sides. When you put the salmon on the pan you will see the colour of the meat progressively change as it cooks. You want to cook it 3/4 of the way on one side and then flip it and cook it for a minute on the other side. Remember not to move the fish around in the pan so it can become golden. Season with salt and pepper.
Remove the salmon from the pan and lower the heat to medium-low.
(At this point it's a good idea to start cooking the pasta. The pasta is cooked in water with plenty of salt until it's al dente. The time varies between 7-10min depending on the pasta. If your pasta is ready before the sauce you can mix it with olive oil so it doesn't stick to each other. Reserve about 1/2 a cup of the pasta water in case you need it)
Add the garlic and lemon zest and cook them for a minute stirring constantly.
Add the Dijon mustard and mix.
Add the white wine and let it evaporate almost completely while stirring constantly.
Add the flour and stir it in.
Add the cream to the sauce little by little off the heat while stirring constantly. Return to the heat until it starts to boil.
Break the salmon with your hands in flakes. Add half of it to the sauce and mix it in.
Add the parmesan cheese and stir to melt it in. Taste the sauce and correct the level of salt and add pepper as well as half the basil.
Add the pasta to the pan with the sauce and mix in to impregnate the flavours. Add pasta water to adjust the texture if it's too thick.
Serve immediately and finish it with extra salmon on top, fried capers, sliced basil and chili flakes.