Use the crinkle-cut blade on a mandolin slicer to cut the potatoes - you will probably need to adjust the blade several times to get the right thickness for the discs, so don't worry if you need to try it a few times.
Take a slice off one potato, then rotate the potato 90 degrees and take off another slice on the same side. Hold the slice up to the light and you should see a lattice pattern with the light shining through the holes. If the slice is too thick, the lattice effect will not work. If you don't see the light, try adjusting the blade to a slightly thinner setting and try again. Once you have created the right thickness, you need to make 48 slices.
Cut out discs from the slices using a 4cm (1.6in) cutter. Dry the discs on kitchen paper.
Place the vegetable oil into a deep, heavy-bottomed saucepan and heat until a small cube of bread sizzles and turns golden in 30 seconds when dropped into it. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Fry the potato discs until they are crisp and golden-brown. Remove and drain them on kitchen paper, and keep to one side in a dry place until you are ready to serve. (Don't try to make them too far in advance or you will lose the all-important texture.) The discs will keep their texture for about four hours if they are stored in an air-tight container.
For the horseradish cream, place all the horseradish ingredients into a clean bowl, mix well and set aside.
Slice the smoked salmon into 48 equal small pieces. Place a piece of the salmon on each of the potato discs. Arrange a sprig of watercress on top of the salmon and spoon a little of the horseradish cream on top of the watercress.
Repeat this process with all of the discs, then place one of the discs on top of another to create a mini-tower. Repeat this process with all the discs.
To serve, place the canapés on a serving plate and dust with a little paprika.