Peel potatoes. Thinly slice using a mandolin or benriner (the slices should be paper thin).: As you work, you will notice the potato slices shimmer with translucent edges and almost whisper when cut. The reason for such thin slicing is to ensure the slices will cook quickly to a crisp without overcooking the salmon inside. If the slices are thicker than paper thin, the exterior will take much longer to brown and the interior salmon may overcook. A common slip here is rushing and producing uneven slices, which leads to patchy browning. Take your time, steady the mandolin, and adjust your grip so each slice matches the last for even results.
Lay out potatoes in a rectangle for each fillet. The slices should overlap and the rectangle should be equal to the length of the salmon fillets and wide enough to wrap over the salmon with a slight overlap.: The laid out arrangement should look like shimmering shingles, with each slice slightly overlapping the next, creating a unified sheet. This overlap is crucial because it creates structural integrity when you fold the sheet over the salmon . You will see a woven texture and the slight translucence where slices double up. If you leave gaps, the salmon will poke through during cooking, so aim for consistent coverage. A frequent oversight is making rectangles that are too small, which leads to exposed fish and uneven crisping.
Brush the potatoes with a light coat of olive oil and top with a piece of salmon. Season the salmon with salt and pepper, then cover with about 1 1/2 tablespoons pesto. Fold the potato slices over the salmon and brush with olive oil. Sprinkle with salt and pepper to taste.: You will feel the gentle give of the wrapped package as it comes together. The light brush of olive oil is what creates those glossy, golden edges when seared. Adding the basil pesto at this stage infuses the fish with its aromatic oils and herbs, which mingle as the potato browns. Smell the burst of basil as you spread the pesto; it helps you gauge how much is enough. Avoid over-brushing with oil, or the potato will fry rather than crisp, becoming too heavy and greasy.
Heat a tablespoon of olive oil in a nonstick skillet. When heated to medium-medium high, place as many wrapped salmon fillets as will fit in the pan without overcrowding. Cook until bottom potatoes are golden brown, then carefully flip to brown the tops and finally the sides. Depending on the thickness of your fillets, the salmon should be cooked after about 10-15 minutes in the skillet.: When the oil shimmers and gives a soft sizzle as you tilt the pan, it is time to add the wrapped fillets. You will hear a satisfying sizzle as the potato hits the pan and begin to smell the nutty, toasted aroma. Patience is key here, allow the bottom to develop a deep golden color before attempting to flip; rushing will tear the shingled crust. Use a wide spatula and take care to support the package while turning, because the seam can come apart if handled too roughly. If the pan is overcrowded, steam will form and the potato will not crisp, so cook in batches if needed. Check the salmon for doneness by looking for flaky flesh and an internal color change rather than relying solely on time.
Serve immediately.: Right after cooking, you will notice a crisp sound when you cut into the shingled crust and the aroma will be at its most vibrant. Serving without delay preserves the contrast between the crunchy potato and tender salmon . The plates will look inviting, with golden edges and a glossy sheen from the olive oil . Waiting too long allows steam to soften the crust, so plan to time plating so guests can enjoy the texture at its peak.