Preheat the oven to 200C/180C Fan/Gas 6.
Sprinkle rock salt onto a roasting tray. Wrap each beetroot individually in foil and place them on the tray – the salt will draw out the moisture. Cook for 1½ hours. Remove from the oven and set aside to cool in the foil — they will steam a little and this will help when it comes to peeling the beetroots. When cool, remove the foil and peel the beetroots. Cut into quarters, and set aside.
Evenly cover the base of a 20cm/8in shallow frying pan with a metal handle with the butter — use your fingers for this, and really get the butter squashed down. Sprinkle the sugar evenly over the butter. Heat the pan over a medium flame until the butter melts and the sugar starts turning a light golden-brown colour.
Place the beetroot quarters on top and arrange in concentric circles on their sides to cover the surface. Set aside to cool.
On a floured surface, roll the puff pastry out to a 3mm/⅛in thickness. Pay attention to the size of it as you are rolling: it will have to cover the beetroots in the pan. Place the puff pastry gently over the beets, tucking any excess pastry in between the beetroot and the pan like a blanket. Brush the pastry with the beaten egg.
Cook the tart in the oven for about 40 minutes, or until it’s golden-brown and oozing caramel slightly at the edges. Remove from the oven, and turn out onto a plate.
Whip the cream in a bowl to very soft peaks, then stir in the goats’ cheese and crème fraîche and whisk again.
Serve slices of the beetroot tart with the goats’ cheese, chicory and dandelion leaves, if using.