Place a rack in the centre of the oven and preheat to 175°C (350°F).

Line a baking sheet with parchment paper and have two more sheets of parchment and another baking sheet at hand.

Stir the olive oil and cocoa together in a bowl and set it aside for the moment.

Stack the filo sheets and cut the pastry in half. You'll work with one piece of filo at a time and should keep the remainder covered with a clean kitchen towel.

Place a piece of filo on the parchment-lined baking sheet, brush it with some of the cocoa-oil, and sprinkle it with 1 to 2 tablespoons of the sugar. Place a second sheet of filo on the first, brush it with cocoa-oil, and sprinkle with sugar. Repeat with one more filo sheet.

Cover the stack with a piece of parchment paper and repeat the stacking, brushing, and sprinkling with the remaining 3 sheets of filo.

Cover the sheets with a piece of parchment paper and top with a baking sheet, which will weigh the filo and keep it from puffing or curling.

Bake the filo for 10 to 12 minutes.

Flip the batch and continue to bake for a further 5 minutes until the sheets are shiny and crispy.

Transfer the baking sheet to a wire rack, remove the top baking sheet and separate the two stacks, allowing the filo to cool to room temperature.

When the filo is cool, each stack should now be fused and feel like one flaky, crispy sheet.

Heat the milk in a saucepan to just below boiling.

Mix the eggs, sugar, salt, and cornstarch in a heatproof bowl and beat them until the mixture becomes pale yellow and slightly thickened.

Slowly pour the milk into the egg mixture, stirring constantly.

Pour the mixture back into the saucepan and gently cook it until it is quite thick. It is important to stir constantly so the mixture doesn't become lumpy.

Remove the saucepan from the heat and stir in the crème fraîche.

Refrigerate the mixture until you are ready to assemble the mille-feuilles.

Break the cocoa filo into shards. Layer the shards alternating with the crème fraîche custard, finishing with a cocoa shard. Add a few fresh strawberries to the plate and shave some dark chocolate over the surface.