Bring a large pot of well-salted water to a boil and cook the pasta until just al dente. Before draining, reserve at least one cup of pasta water.
Heat the olive oil and butter in a wide pan or a wok over medium heat. Once the butter has melted, add the garlic and cook briefly until fragrant. Keep the heat steady so it softens without browning.
Add the salmon in a single layer. Let it cook undisturbed for a couple of minutes, then gently turn the pieces. Cook for a minute only, as they will continue cooking with cream.
Lower the heat slightly and pour in the cream. Let it warm through, stirring occasionally.
Let it gently simmer for a couple of minutes, then add the Parmesan along with salt, pepper, lemon juice, and the chopped herbs.
Add a small amount of the reserved pasta water and stir. The sauce should loosen and turn glossy rather than thick. Add the drained pasta.
Toss gently so the salmon stays in soft pieces. Stir in more pasta water as needed until the sauce coats everything evenly.
Finish with extra lemon juice and chopped herbs. Toss once more and serve straight away.