Fill a large pot with water and add the olive oil, cook the spaghetti according to the package instructions. Remove from heat. Drain the noodles using a colander and return them to the warm pot. Cover with a lid so that they remain warm.
Take an ounce of the smoked salmon and mince it finely. This will be added to the pasta sauce.
In a medium bowl, combine the minced salmon, butter, cheese, chives and dill. Mix until well incorporated.
Add the butter mixture to the pot of cooked pasta, return the pot to the stovetop and heat on low, stirring the butter into the noodles until it's melted.
Add cream and flake the smoked salmon into small pieces, gently folding it into the noodles.