In a large pot, melt the butter over medium heat. Add the chopped onion and minced garlic, and sauté until they become translucent and fragrant.
Add the eel slices to the pot and cook for a few minutes on each side until they start to brown slightly.
Pour in the white wine and let it simmer for a couple of minutes to reduce slightly.
Add the fish or vegetable stock, chopped parsley, chervil, thyme sprigs, and bay leaves to the pot. Stir everything together.
Reduce the heat to low, cover the pot, and let the eel simmer in the herb sauce for about 30-40 minutes, or until the eel is tender.
If you prefer a thicker sauce, you can mix the flour with a little bit of water to create a smooth paste. Stir this mixture into the pot and let it cook for an additional 5 minutes to thicken the sauce.
Season with salt and pepper to taste.
Serve the Paling in 't groen hot with crusty bread or over a bed of cooked rice. Enjoy!