If the salmon you're using has the skin on, use a sharp knife to carefully remove the skin. Don't worry if it isn't the cleanest cut, as the salmon will be broken up later.
Slice the salmon in half if it is one large piece.
Finely mince the shallot and the cloves of garlic.
Bring a large pot of salted water to a boil and cook pasta according to package instructions, and reserve about ¼ cup of pasta water, just in case.
In a large pot or pan, add olive oil over medium heat. Add the shallots and sweat until slightly translucent, then add the garlic and saute until fragrant.
Deglaze the pan with the white wine and use a wooden spoon to scrape the "fond" (aka the brown bits) off of the bottom. Stir to combine.
Add salt and pepper and let it simmer until the wine is reduced by at least half, then add the cream and stir to combine.
Gently lay the salmon pieces in the sauce and cover to let it steam a bit. Then, gently stir in the slightly simmering sauce to help cook the salmon more, it's ok if it breaks apart (it should).
Add the cooked hot pasta to the pot of sauce. Gently stir to combine pasta with the sauce and break apart any unbroken salmon until it is in small chunks.
If the pasta is too dry, add ¼ more heavy cream and a splash of pasta water.
Mix in the grated parmesan cheese and more salt and pepper (to taste), along with the butter. Stir until butter and cheese are melted.
Serve hot and garnish with basil and more grated or shaved parmesan.
Add a squeeze of lemon on top, if you wish.