Heat the butter in a pan. Sauté the shallots and beetroot for approx. 2 mins. Add the balsamic, stir in the thyme, season with salt and allow to cool.
Place two sheets of pastry on a sheet of baking paper, place another two sheets of pastry on top at an angle to create eight corners. Place the pastry in the tin along with the baking paper, brush the base with butter. Spread the beetroot filling on top of the pastry base, top with the cheese and nuts. Fold in any protruding corners. Unfold the remaining four sheets of pastry, brush with a little butter, gather the edges individually, place on top of the mixture. Top with the knobs of butter and a pinch of Fleur de Sel.
Bake for approx. 30 mins. on the bottom shelf of an oven preheated to 200°C, cover with foil towards the end of the baking time if necessary. Remove the cake from the oven, allow to cool slightly, remove the tin frame, slide onto a platter and serve warm.