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Step 1
Preheat oven to 200C. Cut a 25cm square from each sheet of pastry, place each square on a baking tray lined with baking paper and prick all over with a fork. Place a 2cm high cutter in each corner of each tray, place baking paper over the cutters and place another tray on top (this helps the pastry rise evenly). Bake, swapping and turning trays partway through cooking so pastry cooks evenly, until dark golden and puffed (10-15 minutes). Cool on wire racks, then trim to 20cm squares with a serrated knife and place one square in the base of a 20cm-square cake tin lined with baking paper that extends above the rim for easy removal.
Step 2
Bring milk, cream, butter and vanilla beans and seeds just to the simmer in a saucepan over medium-high heat. Meanwhile, whisk sugar, cornflour and yolks in a bowl to combine. Pour milk mixture in, whisking continuously, then return to pan and whisk until thick (4-5 minutes). Remove from heat, discard vanilla beans and pour onto pastry in cake tin. Press remaining pastry square on top and refrigerate until set (2-3 hours).
Step 3
For vanilla icing, stir ingredients in a bowl until smooth, adding a little water to thin to drizzling consistency.
Step 4
Remove vanilla slice from tin and carefully cut into rectangles with a serrated knife. Drizzle with vanilla icing and serve.