Generously season both of the salmon fillets with salt and pepper.
Add to a non-stick pan over medium-high heat in a small drizzle of olive oil. Once golden on the bottom side, flip over and place a sprig of dill on top of each fillet. Melt 1 heaped tbsp butter into the pan and baste the salmon until golden on the other side and just about cooked through the centre. Remove and place to one side. Break up into large chunks just before needed (discard dill).
Cook the pasta in salted boiling water until al dente, reserving a cup of starchy pasta water. Drain when needed.
Lower to medium heat and fry the shallots in the leftover brown butter until soft and deep golden, then fry the garlic for a further minute or so.
Pour in 1/3cup/80ml wine and leave to simmer for a good 4-5mins to reduce, deglazing the pan as necessary. Reducing the wine is important so it burns off the alcohol and doesn't end up too bitter. Once almost completely reduced/evaporated, stir in 3/4cup/180ml heavy/double cream.
Stir in 1 tsp finely diced dill, 1 heaped tbsp finely diced parsley and a small squeeze of lemon juice to taste (careful, you won't need much). Season with salt and pepper. Keep on a gentle simmer.
Toss through the pasta until the sauce clings to it, adding a dash of starchy pasta water if you needed to loosen up the sauce. Add salmon and gently toss to combine.
Serve with parmesan & parsley and enjoy!