Transfer the beetroot to a tray lined with baking paper.
Bake for approx. 1 hr. 10 mins. in the lower half of an oven preheated to 200°C. Leave the beetroot to cool, peel and set aside.
Heat the oil in a non-stick frying pan. Fry the mushrooms in batches for approx. 5 mins., stirring occasionally. Reduce the heat, add the onion, cook for a further 5 mins. Add the balsamic, continue to cook until the liquid has completely evaporated. Mix in the prunes, nuts and sage, season.
Roll out the dough on the baking tray, cut a strip (approx. 5 cm wide) from one of the narrow ends and chill. This strip will be used for decoration. Spread 3/4 of the filling over the dough, leaving a border of approx. 7 cm all the way around. Place the beetroot next to each other in the middle of the dough. Spread the remainder of the filling between the beetroot, press down gently. Brush the edges of the dough with egg white, fold loosely over the beetroot, press down. Cut circles out of the chilled strip of pastry, brush with egg white, use to decorate the pastry, chill for approx. 30 mins. Whisk together the egg yolk and water, brush the dough with the egg wash.
Approx. 35 mins. in the lower half of an oven preheated to 220°C. Remove from the oven, cut into slices.
Combine the balsamic and oil, drizzle over the slices, sprinkle with fleur de sel.