Preheat the oven to 200C (400F / Gas Mark 6). Brush two of the sheets of filo generously with the melted butter and top each one with another sheet. Cut each one into rectangles and dust with the icing sugar. Arrange on a non-stick baking sheet and bake in the oven for 8 minutes until golden brown. Leave aside to cool.
To make the lemon crème pâtissière, bring the lemon zest, juice and sugar to the boil in a small pan and mix the butter in until melted and smooth. Meanwhile, whisk the eggs in a large bowl to combine and slowly add the lemon mixture, whisking all the time. Return the mixture to the pan and cook gently over a low heat, stirring continuously, until smooth and thick. Cover the surface with cling film and leave to cool. Refrigerate until ready to use.
Next, cut about a quarter of the strawberries into quarters and place in a medium pan with the icing sugar. Cook gently over a low heat until softened. Add the remaining strawberries and the red currants also and continue to cook until warmed through but the additional fruit retains their shape. Remove from the heat and leave to cool.
Meanwhile, make the coulis. Bring the sugar and water to the boil in a small pan, stirring throughout. Reduce to simmer for 2 minutes and then leave to cool completely. Blitz the cooled syrup in a blender with the strawberries and lemon juice until smooth. Pass through a fine sieve and reserve.
Build each Mille feuillé into layers on each serving plate. Start with a piece of crisp filo. Fill a piping bag set with a nozzle with the crème patisserie and pipe onto the filo. Spoon some of the cooked fruit mixture on top and place another filo piece on top. Repeat with another layer of everything, finishing with the pastry again. Drizzle the coulis around and serve.
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