To begin, pat the eel pieces dry with paper towels. Lightly season with salt and black pepper. This helps the fish retain its delicate flavour and enhances seasoning absorption.
In a large pan or Dutch oven, melt the butter over medium heat. Add the chopped shallots and sauté for 2–3 minutes until softened but not browned. This step builds the base flavour for the sauce.
Pour in the white wine and fish stock. Stir in the bay leaf and white wine vinegar. Bring the mixture to a gentle simmer. The acidity in the wine and vinegar will balance the richness of the eel.
Gently place the eel pieces into the simmering liquid. Cover with a lid and let it cook for about 15–20 minutes over low heat. The eel should become tender but still hold its shape. Stir occasionally to ensure even cooking.
Meanwhile, finely chop all the fresh herbs. For the most vibrant sauce, mix the herbs just before adding them to preserve their fresh, grassy aroma.
Remove the cooked eel from the pan and set aside on a warm plate. Discard the bay leaf. Turn off the heat and add the chopped herbs and spinach into the cooking liquid. Stir well, letting the residual heat gently wilt the greens.
Using a handheld blender, puree the herb sauce until smooth. If a thicker consistency is desired, let the sauce simmer for an additional 2–3 minutes. Adjust seasoning with salt, pepper, and an extra dash of vinegar if needed.
Return the eel to the pan, coating it in the green sauce. Serve immediately with crusty bread, crispy fries, or boiled potatoes. Garnish with a lemon wedge for a fresh citrus kick.