Roll out the pastry and use it to line a 23cm loose bottomed pie tin. Line with greaseproof paper and fill with baking beans. Bake blind for 20 minutes.
Whilst the pastry is baking, prepare the filling by pureeing the beetroot along with the eggs in a food processor.
In a small saucepan add the sugar, all the spices and cream and bring slowly up to a simmering point. Pour into the food processor and mix thoroughly with the beetroot puree.
Remove the pastry case from the oven and reduce the temperature to 180°C/Gas Mark 4.
Pour the filling carefully into the pastry case and bake for around 25-30 minutes. The edge should be puffed up a little and the centre will still be a touch wobbly. Allow to cool and chill in the fridge. Serve with crème fraiche.