Clean the fish fillets, season with salt and pepper, and drizzle with lemon juice. Let them rest for 10 minutes.
Heat a skillet over medium heat. Add 1 tablespoon of olive oil and the butter. Sear the fish fillets for 3-4 minutes on each side, or until golden brown. Set aside.
To make the dill sauce, melt the butter in a small saucepan. Stir in the flour and cook for 1-2 minutes, stirring constantly, to create a roux.
Gradually whisk in the water, ensuring a smooth consistency. Stir in the sour cream and finely chopped dill. Season with salt and pepper to taste.
Simmer the sauce over low heat for 5 minutes to allow the flavors to meld.
To serve, place the pan-seared fish fillets on a plate, drizzle with the dill sauce, and serve with a fresh salad or cooked rice.
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