For the pastry shell: sieve the flour and icing sugar into a bowl. Add the cubes of butter and work them into the flour with your fingers, as you would for a crumble. Mix 1 egg with 1 tablespoon of milk and add them to the flour. Fold all the ingredients together until you get a dough but don’t knead it too much; it should have a crumbly texture, as opposed to a smooth and elastic one. Shape the dough into a ball, flatten it over a floured surface, cover generously with flour, then wrap in cling film and store in the fridge for 30 minutes to an hour.
Remove the pastry from the cling film and roll over a well-floured surface, into a 1 cm thick disk, large enough to cover your pie dish and extend over the sides. Carefully place the pastry over the pie dish and fit it with your hands; trim the excess edges at the top, leaving a small amount to extend over the dish as the pastry will shrink during baking. Cover this with buttered baking paper (butter side facing the pastry) and then top with rice or ceramic beads. If you can, cover the edges of the pastry with foil, to prevent them from burning. Bake at 180° C for 15 minutes.
For the basil custard: heat the milk and double cream until the mixture becomes foamy. Add the sliced basil leaves and simmer the mixture on a low heat for 5 minutes. Strain this mixture to separate the basil from the milk. At this point you can add the basil to a food processor with 2 tbsp of the milk and cream and puree the mixture. Add half of the basil puree to the rest of the milk and discard the other half. Whisk the eggs and caster sugar together until well combined. Add the hot basil and milk infusion to the eggs and sugar, whisking continuously.
To assemble the tart:remove the pastry from the oven and carefully lift the baking paper and rice/beads. Poor the custard mixture into the pastry shell. Cover the entire dish loosely with foil, to prevent browning and return to the oven; bake for 40 minutes at 180° C. Check that the custard is completely set before removing from the oven. Let the custard tart cool completely before decorating with strawberries. You can enjoy it straight away; keep the remaining tart refrigerated and serve within 24 hours.