To make the gaufrette potatoes, adjust the mandoline so that the ridged blade is exposed by about 1/8 of an inch. Remove the potato from the water and pat dry with a paper towel. Hold the potato at an angle of 45 degrees, and run the potato over the ridged blade of the mandoline. (The first slice will not be usable, so discard it.) Turn the potato sideways 45 degrees in the opposite direction, this will make your first waffle-cut potato slice. Repeat the process, turning the potato after each pass over the blade to maintain the waffle-cut. Place the potato slices in cold water to keep them from oxidizing. Heat the oil to 350 degrees F in a 1-gallon pot.

Working in batches, add the potato slices a few at a time to the hot oil. Turn occasionally to ensure even browning, and cook until golden brown and crispy, about 3 to 4 minutes. Using a slotted spoon or strainer, remove the chips from the oil and place on a paper-lined plate and sprinkle with the salt. To assemble the dish, cut the gravlax slices into small 1 to 2-inch length pieces and arrange 1 piece of gravlax on top of each potato chip. Top each chip with a small dollop of sour cream, and place 1/4 teaspoon or more of caviar on top of the sour cream. Garnish with a small sprig of fresh dill, and serve.