Preparation

• Finely zest the lemons using a rasp-style grater. Cut the top and bottom ends off the lemons, then stand each on a cut end and slice off the remaining peel to expose the flesh. (Try to remove all of the bitter white pith.) Working over a bowl, cut the lemon segments from the membranes, then cut each segment in half. Squeeze the membranes into a small bowl, and reserve the juice.
• Heat a large, straight-sided skillet over medium heat. Add the butter, oil, onion, and 1/2 tsp. salt. Cook, stirring occasionally, until the onion just starts to soften, 2 to 3 minutes. Add the lemon zest, segments, and juice. Reduce the heat to low and cook, stirring occasionally, until the onion is very tender and the lemons are breaking down, 5 to 8 minutes. Raise the heat to medium high and add the fish stock, thyme, and bay leaf; reduce the heat to low, and simmer until fragrant, 20 to 30 minutes.
• Season the fish with salt and pepper. Gently slide the fish into the poaching broth and cook over medium-low heat at a very gentle simmer, occasionally basting the top of the fish with the liquid, until cooked through, 5 to 8 minutes. Discard the thyme and bay leaf.
• Using a fish spatula, divide the fish among four shallow bowls and evenly distribute the broth around the fish. Garnish each bowl with the chives and a drizzle of oil.