Preheat the oven to 200C/400F/Gas 6.
For the pastry, mix the flour and icing sugar together in a bowl. Add the butter and rub it in lightly with your fingertips until the mixture resembles fine breadcrumbs. Alternatively, do this in a food processor or a mixer and then transfer to a bowl.
In a small bowl or jug, mix the egg with the lemon juice and two tablespoons of water. Make a well in the centre of the flour mixture and pour in the egg mix. Using a table knife, work the liquid into the flour to bring the pastry together. If it seems too dry, add a splash more water. When the dough begins to stick together, use your hands to gently knead it into a ball. Wrap in cling film and rest in the fridge for at least 15 minutes.
Roll out the pastry on a lightly floured work surface to about a 3mm/⅛in thickness. Line a 23cm/9in tart tin with the pastry, leaving any excess pastry hanging over the edge. Reserve a little uncooked pastry in case you need to patch any cracks later.
Line the pastry case with baking parchment or foil, then fill with baking beans, or uncooked rice or lentils. Bake blind for 15 minutes, then remove the parchment and baking beans and return to the oven for about eight minutes or until the pastry looks dry and faintly coloured. Using a small, sharp knife, trim away the excess pastry from the edge. Use a tiny bit of the reserved raw pastry to patch any cracks or holes if necessary.
Turn the oven down to 180C/350F/Gas 4.
For the filling, if you’re using pre-packed beetroot, drain away any excess liquid. Roughly chop the beetroot and put into a food processor with the cream. Blend to a thick purée.
In a bowl, whisk the eggs and sugar together thoroughly. Add the beetroot purée, spices and lemon zest and mix well.
Pour the mixture into the pastry case and bake for 30–40 minutes, or until the filling is set with a slight wobble in the middle. Leave to cool completely.