Pour the oil into a jug that will fit the heat of your stick blender.: The oil should be at room temperature and poured into a container tall enough to immerse the head of your stick blender, which helps form a steady emulsion. When you position the blender properly, you will hear a humming, and the oil will begin to thicken as air is incorporated. The visual cue is the mixture becoming opaque and glossy. If your container is too wide, the blender head may not reach the oil properly and the emulsion can fail, so choose a snug vessel.
Add in the Dijon mustard, lemon juice, salt, pepper and tarragon.: These aromatics and acids are the backbone of the mayo, and adding them before the egg helps set flavor parity. You will notice a bright, herby scent as the tarragon meets the acid. The mustard gives slight grain and tang that stabilizes the emulsion. A common mistake is underseasoning now and trying to correct after the oil is added, which is harder to balance.
Then carefully crack the egg in, be careful not to break the yolk.: Keeping the yolk intact initially helps you position the blender head over it for a clean start. The yolk carries lecithin which is essential for emulsification. When you crack the shell gently, you preserve the yolk for a controlled beginning. Broken shells or a yolk with white mixed in can make it trickier to start a glossy mayo.
Place the head of the stick blender over the yolk and then turn the speed to high and slowly bring the blender up through the oil.: Start with the blender head resting at the bottom so the yolk, mustard, and acid can emulsify with a small amount of oil, then lift slowly as the mixture thickens. You will feel the viscosity change under the blender and see a transformation to a creamy, homogeneous texture. Pulling the blender out too quickly or pouring oil too fast are the principal causes of a broken emulsion, so move steadily.
You should have a glossy tarragon mayonnaise within seconds.: A successful emulsion will look silky and chant a mild sheen under light, and the aroma of tarragon will be more pronounced. The mayonnaise should cling to a spoon in a ribbon. If it looks separated or watery, you can rescue it by starting with a fresh yolk and slowly whisking the broken mayo into it.
Mix the tarragon together with the mayo and add a spritz of lemon juice.: Folding in the remaining chopped tarragon releases herb oils into the mayonnaise and the final lemon juice brightens it. You should smell fresh herb notes and a lifted citrus edge. Overworking the mixture will bruise herb leaves, releasing bitter notes, so fold gently.
Mix the flour, salt and white pepper together in a shallow bowl.: Combining these dry seasonings creates an even coating for the fish , ensuring each fillet picks up a balanced amount of seasoning. The texture will be fine and powdery, and the aroma will be lightly seasoned. Dumping flour directly onto a wet fillet can clump, so keep the bowl shallow for controlled dredging.
Add each fillet of fish and give it a light dusting of the flour.: Press the fillet into the flour briefly so a thin film forms, shaking off excess to avoid a cakey exterior. You will see the surface go matte with a delicate dusting, and this layer will crisp in the pan. Too much flour is a frequent misstep that yields a gummy rather than crisp crust.
Place a large heavy based fry pan over a medium heat and add the olive oil. Once it is hot, add the fish and cook for 2 minutes on each side.: The pan should be hot enough that the oil shimmers, producing an immediate sizzle when the fillet lands. You will hear a lively hiss and see edges take golden color after about two minutes, creating a slight crust while the inside stays flaky. If the pan is not hot enough, the fish will steam and fail to brown properly, so preheat thoroughly.
Turn the heat on the fry pan up to high and once it is smoking hot add the lettuce leaves and the extra virgin olive oil.: At this point the pan should produce thin wisps of smoke, and adding the leaves will make them sizzle and char quickly. The leaves will collapse slightly and develop glossy, darkened patches. Work fast because overexposure to high heat will char them to a bitter black.
Allow the lettuce to char and spit. Once it has some colour and is glossy from the oil, remove from the pan and sit it on top of the fish.: The charring gives a nutty, smoky edge and the surface will glisten from the oil. Placing the hot, charred lettuce on the fillet allows residual heat to mingle. Leaving the leaves on the pan too long will make them papery and dry rather than pleasantly wilted.
Add the lemon to the pan, cut side down and turn off the heat. Leave the lemons to char whilst you assemble the burger.: The cut lemon will take on caramelized notes and a caramel scent as it rests in the warm pan. These wedges are ideal for squeezing over the finished sandwich. Keep an eye on them, because if the pan is too hot they can char to an acrid bitterness.
Add a good layer of the mayo to the bottom of each bun. Add a fillet of fish and two charred lettuce leaves.: The mayo should be creamy and slightly tangy, providing a silky counterpoint to the warm fish and smoky lettuce . Assemble quickly so the roll soaks up just a hint of sauce without collapsing. Overloading the bun with sauce can make it soggy rather than luxurious.
Remove the charred lemon wedges from the pan and serve immediately.: Serving right away preserves the textural contrast between warm, crisp fish and the glossy lettuce. A final squeeze of the hot charred lemon over the sandwich brightens every bite. Delaying service will cause the bun to soften and the charred edges to lose their appeal.