Heat a non-stick skillet over medium-high heat and add olive oil and butter. Season the salmon fillets with salt and pepper, then place them skin-side up in the pan. Sear for 3-4 minutes until the skin is golden and crispy. Flip the fillets gently and cook for an additional 2 minutes until just cooked through, then remove the salmon from the pan and set aside.

In the same skillet, reduce the heat to low and add chopped shallots. Sauté for 2-3 minutes until the shallots are soft and translucent. Next, add minced garlic and lemon zest, stirring for about 30 seconds until fragrant. Pour in the chicken stock, scraping up any flavorful bits stuck to the bottom of the pan, and let it simmer for 10 minutes to develop the sauce's foundation.

After the stock has simmered, stir in the crème fraiche or heavy cream, allowing it to combine smoothly, and then sprinkle in the fresh dill. Increase the heat slightly and let the sauce bubble gently for about 5 minutes, stirring occasionally, until it thickens and becomes creamy. Taste and adjust seasoning with salt as needed.

Return the seared salmon to the skillet, nestling it into the creamy sauce. Reduce the heat to low and let it simmer for 5-7 minutes, allowing the flavors to meld and the salmon to heat through. The salmon should be opaque and flake easily, ensuring it’s perfectly cooked while the sauce achieves your desired consistency.