Pat the salmon fillets with a paper towel to remove excess moisture.
In a shallow bowl combine the semolina flour or all-purpose flour, dill, salt and pepper.
Dredge the fillets in the flour mixture, shake off the excess and place the fillets on a plate.
In a large skillet set over medium-high, heat the oil and place the fillets into the skillet. Cook the salmon for 4 minutes, flip and cook an additional 2 minutes (for medium rare) or according to your preference.
Remove the salmon fillets, place on a plate and cover with foil to stay warm.
For the Lemon Sauce:
Melt 2 tablespoons of the butter in the skillet and sauté the shallots until soft and translucent, about 1-2 minutes. Add the garlic and cook for 30 seconds until fragrant.
Add the remaining tablespoon of butter to the skillet and when it has meted sprinkle the flour over the shallot/garlic mixture. Stir and cook for 1-2 minutes; then pour in the wine stirring to remove any bits stuck on the bottom. Pour in the chicken broth, lemon juice, capers and lemon slices. Bring the sauce to a boil and immediately reduce to low and simmer the sauce for 5 minutes.
Whisk in the cream and simmer for another minute.
Add the salmon fillets back to the skillet, spooning sauce over them and simmer for another minute.
To serve:
Spoon a puddle of the sauce into individual pasta bowls and add a portion of cooked linguine.
Place a salmon fillet and lemon slices on each serving, add more sauce over the salmon and pasta and garnish with chopped parsley or fresh dill sprigs.
Notes
Cooking time for the salmon will depend on the thickness of the fillets.
Be sure to rinse and drain the capers as they are preserved in a salty brine.
Other options for pasta would be spaghetti, fettuccini, bucatini or pappardelle