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Make the pastry by putting the butter and flour in a food processor and pulsing to a crumbly mixture. Tip in the sugar and egg yolk, and pulse to a dough. Wrap in cling film and chill in the fridge for at least 1 hr. Roll out the dough on a floured surface to the thickness of a £1 coin, then drape over a 12 x 35cm rectangular tart tin, press into the sides, and chill for 30 mins.
Heat oven to 180C/160C fan/gas 4. Line the pastry case with parchment and baking beans. Bake for 25 mins until the pastry is a light biscuity colour. Remove the beans and parchment; if needed, bake a little longer just to crisp up the base.
While the pastry is cooking, bring the milk, sugar and vanilla to the boil. Whisk the eggs and flours together, then pour over the milk, whisking as you pour. Return the mix to the pan and cook until it becomes a thick and glossy custard. Pass it through a fine sieve and leave to cool. Meanwhile, whisk the cream until it holds its shape. Fold the cream and custard together.
When the tart case is cool, spread the custard over the base. Slice the strawberries and arrange them over the top. Bring the jam to the boil with a few tbsp water, simmer to a smooth glaze, then brush over the strawberries. Scatter over the basil leaves and serve.