In a non-stick skillet, heat the olive oil and butter over medium-high heat. Allow the fats to melt and shimmer together, creating a rich base for searing. This step should take about 1-2 minutes.

Pat the salmon fillets dry and season them with salt and pepper on both sides. Place them skin-side up in the hot pan and cook for 3-4 minutes until they develop a golden color. Flip the fillets and cook for an additional 2 minutes.

In the same skillet, lower the heat to medium and add the chopped shallots. Sauté them for 2-3 minutes until soft and translucent. Stir in the minced garlic and lemon zest, cooking for another 30 seconds.

Pour in the chicken or fish stock, using a wooden spoon to scrape any browned bits from the bottom of the pan. Bring the mixture to a simmer and let it cook for about 10 minutes.

After simmering, lower the heat and stir in the crème fraiche or heavy cream along with fresh dill. Let the sauce simmer gently for an additional 5 minutes.

Return the cooked salmon fillets to the skillet, ensuring they are nestled into the creamy lemon dill sauce. Cover and let everything simmer for 5-7 minutes until the salmon is fully cooked through.