Boil the potato in 625ml (21fl oz/2½cups) water for 10 minutes, or until very soft. Drain well, reserving the potato water. Cool for 5 minutes, then mash the potato until very smooth.
Grease and lightly flour a baking tray. Put the yeast and 125ml (4fl oz//2cup) warm water in a small bowl and stir well. Set aside for 10 minutes.
Put the oil, eggs, yolks, honey, 125ml (4fl oz/½cup) reserved potato water, mashed potato and ½teaspoons salt in a large bowl and beat with a wooden spoon until smooth. Leave to cool. Add the yeast mixture and gradually mix in 250g (9oz/2cups) of the flour, beating until smooth. Add another 185g (6½oz/1½cups) flour and mix until a rough soft dough is formed. Knead the dough for 10 minutes, incorporating the remaining flour as required, to keep the dough from sticking. Place the dough in an oiled bowl and brush the surface with oil. Cover with plastic wrap and leave in a draught-free place for 1½ hours, or until doubled in size.
Turn the dough out onto a floured work surface and knead for 4 minutes. Divide into two, a one-third portion and a two-thirds portion, then divide each portion into three equal parts. Leave to rest for 10 minutes. Roll each part into ropes about 35cm (14inches) long, with the centre slightly thicker than the ends. Braid the three thicker ropes, pinching the ends together, and place on the tray. Whisk the extra egg yolk and 1tablespoon water and brush over the challah. Repeat with the remaining three ropes and place on top of the first braid, making sure the ends of the braids overlap. Secure tightly and brush with some of the egg glaze. Cover with plastic wrap and leave in a draught-free place for 30 minutes, or until doubled in size. Preheat the oven to 180°C (350°F/Gas 4).
Brush the dough with the remaining glaze and sprinkle with the seeds. Bake for 50–55 minutes, or until golden brown. Cool on a wire rack.