Add the flour and a pinch of salt into a food processor and pulse until combined. Add the butter to the flour and pulse briefly until only just combined. There should still be visible pieces of butter.
Drizzle over 2 tbsp ice-cold water and pulse until you have a firm, rough dough. If the dough seems too dry, add more water 1 tbsp at a time until you have the right consistency. Tip out on to a lightly floured surface and gently bring together into a rough rectangle, then wrap in clingfilm and chill for 20 minutes.
Turn the dough out on to a lightly floured work surface. With the shortest edge towards you, roll the dough in one direction only until approximately 8cm x 45cm. Keep the edges as straight and even as possible and don’t overwork the butter – you should have a visible marbled effect.
Fold the top third down to the centre, then the bottom third up and over that so it’s a bit like an envelope. Give the dough a quarter turn and roll out again to three times the length, with the shortest edge towards you. Fold the pasty as you did before, wrap with cling film and chill for at least 25 minutes.
Lightly flour your work surface and scatter over a little caster sugar. Remove the pastry from the fridge and place on the floured surface, then roll out into a rectangle approximately 20cm x 35cm in size. Line a large baking tray with baking paper and scatter with more sugar. Using a rolling pin, lift the pastry on to the baking paper. You might need to trim the ends of the pastry slightly if it’s too large for the tray.
Scatter more caster sugar over the pastry and cover with another sheet of baking paper. Lay another heavy baking tray on top, then bake for 28-30 minutes until the pastry is golden and crisp. Set aside to cool.
While the pastry cools, get to work on the filling. Grate the chocolate on to a plate and transfer to a fridge immediately to prevent it melting. Whip the cream along with the 2 tbsp of caster sugar until soft peaks form, then whip in the mascarpone and vanilla extract. Fold the strawberries through then cover, move to the fridge and leave until needed.
Once the pastry is completely cool, trim the edges to create a 16cm x 30cm neat rectangle. Cut into 12 equal rectangles by cutting one and using it as a guide for the next rectangles by laying it on top of the pastry.
When you’re ready to assemble, lay down one rectangle of pastry and add a couple of spoonfuls of the cream and strawberry mix. Smooth with the back of a spoon and use a teaspoon to sprinkle over some of the grated white chocolate. Place the second pastry layer on top and gently press down. Add more of the cream mixture and another sprinkling of the white chocolate. Add the final pastry layer and press down gently so that the cream bulges out slightly. Repeat with the remaining pastry layers until you have 4 millefeuille.
Use a palette knife to smooth the filling out at the sides, filling any gaps. Dust each millefeuille with the icing sugar and serve.