Preparation
Combine flour, 1/2 tsp. salt and 1/4 tsp. pepper in a shallow dish. Dredge fish in flour. Heat 2 tsp. of the oil in a Dutch oven or large sauté pan. Swirl the pan to coat the bottom evenly with oil, then add fish. Cook, turning, just until lightly browned, 2 to 3 minutes. Transfer the fish to a plate and set aside.
Add the remaining 1 tsp. oil to the pan and reduce heat to medium. Add onions and garlic and cook until softened, about 2 minutes. Slowly pour in wine and bring to a boil. Add stock or clam juice and water; bring to a boil. Add potatoes and carrots and return to a boil once again. Cover and cook over medium heat until the vegetables are just tender, about 20 minutes.
Return the fish to the pan, reduce heat to low and cook, covered, until the fish is opaque in the center, 5 to 10 minutes longer. With a slotted spoon, transfer the fish and vegetables to a plate and keep warm.
Increase the heat to high and boil the cooking liquid for 5 minutes to intensify the flavors. In a medium-sized bowl, whisk together egg, 3 Tbsp. lemon juice and dill or fennel. Gradually whisk a little of the hot cooking liquid into the egg mixture, then pour the egg mixture into the remaining cooking liquid in the pan. Cook over medium heat, stirring constantly, until slightly thickened (do not boil), 1 to 2 minutes. Return the fish and vegetables to the pan and warm through. Taste and adjust seasonings, adding more lemon juice, if desired.