Pre-heat the oven to 390f / 200ºc.
Peel and top and tail the beetroots and cut them into ½ cm slices. Put on a roasting tray and sprinkle with a table spoon of caster sugar and a good pinch of salt. Place in the oven for about 20mins. Test with a knife - they should be soft with little resistance, and put to one side to cool.
Put the sliced onions into a saucepan and add the balsamic and red wine vinegar, along with the olive oil and 3 tablespoons of caster sugar. Put on a medium heat and stir occasionally until the liquid has evaporated. This should take about 30 minutes. Leave to one side to cool.
Lightly grease the dish you will be baking the tart in.
Take a sheet of filo and place it your dish so that the pastry comes up the sides slightly (fold the edges over if needed). Gently brush with some beaten egg and sprinkle over a small amount of the crushed walnuts. Lay another piece of filo over the top and repeat the process until you have placed on your last layer of filo. Brush well with the beaten egg and put in the oven for 10mins. Once golden brown, leave to one side to cool.
Turn the oven down to 355ºf / 180ºc.
In a bowl, whisk together the eggs, creme fraiche and chives. Add salt and pepper to taste. Cut the gorgonzola into small cubes and stir in to the egg and cream.
Take the filo case, and evenly spread over the onion mixture. Place the roasted beetroot slices on top and then pour over the egg and cream mixture. Pop in the oven for 40mins, until the filling has set and the top is golden brown. Let cool before serving.