In a bowl, mix the flour with all the other ingredients up to and including the salt. Pour in the water, add the honey, knead into a soft, smooth dough using the dough hook on a food processor for approx. 5 mins. Cover and leave to rise at room temperature for approx. 1½ hrs.
Divide the dough into 6 pieces, shape into balls. Lightly flour the handle of a wooden spoon and make a hole in the centre of each. Allow the dough rings to form around the spoon handle until the opening measures approx. 4 cm in diameter. Place the bagels on a baking tray lined with baking paper, cover and leave to rise for approx. 15 mins. Cook the bagels in batches in simmering salted water for approx. 30 secs. Remove with a slotted spoon, drain thoroughly and return to the baking paper. Mix the egg yolk with the water, salt and sugar, coat the bagels with the mixture, sprinkle with the flakes.
Approx. 25 mins. in the centre of an oven preheated to 200°C. Remove from the oven, leave to cool on a cooling rack.
Heat the clarified butter in a non-stick frying pan. Crack the eggs one at a time, slide carefully into the frying pan, then fry over a low heat until the egg yolks are covered with a layer of white. Carefully turn the fried eggs with a spatula, fry until golden. Cut the bagels in half crosswise. Combine the mayonnaise and mustard, spread over the bagel bases. Place the fried eggs, pastrami, gherkin and sprouts on top, cover with the top half of the bagel.