1: First make the ice cream. Put the strawberries in a large pan and gently stew them over a very low heat for 15–20 minutes, stirring from time to time, until they have broken down – you don’t need to add any water. Tip them into a blender or food processor and whizz until smooth. Pass them through a fine sieve and leave to cool. Weigh out 500g of the purée (if you have any left over, it’s delicious used to dress a fruit salad or with yoghurt). Mix it with the single cream and sugar. Place this mix in an ice-cream machine and churn until frozen. Scrape into a freezer container, seal and freeze until needed. Remove from the freezer about 10 minutes before you want to serve it.
2: Make the pastry. Cream together the butter and sugar in a stand mixer with the beater attachment. When smooth, reduce the speed and slowly add the flour and start to bring to a paste. Just before it comes together completely, add the egg. When it has just come together into a paste, remove from the bowl and wrap in cling film. Refrigerate for at least 1 hour, or overnight.
3: Preheat the oven to 170°C/Gas Mark 3.
4: Roll out the pastry on a lightly floured surface to the thickness of a £1 coin. Cut out circles and line six 10cm loose-bottomed tart tins, pushing the pastry in tightly. Let the excess hang over the sides. Line each tart with several layers of cling film or baking parchment and fill with baking beans or uncooked rice or pulses. Place on a large baking sheet and cook for 20–25 minutes, until the pastry looks crisp and golden. Remove the beans and cling film and bake for a further 5–8 minutes to make sure the tartlet shells are dried out and have an even colour. Leave to cool.
5: To make the crème patissière, bring the milk to the boil in a medium saucepan. In a mixing bowl or a stand mixer, whisk the egg yolks and sugar until light and fluffy, then whisk in the flour. Pour on the hot milk, whisking constantly, and then pour the mixture back into the pan. Cook over a gentle heat, stirring until it thickens, and continue to cook for a further 2–3 minutes to cook out the flour. Remove the crème patissière from the heat and pour into a stand mixer with the paddle attachment. Add the balsamic vinegar and turn on to a slow speed. Keep mixing until it cools down to a smooth paste. Add the cracked black pepper, put into a container, cover and refrigerate until needed.
6: To make the glaze, put all of the ingredients into a saucepan, bring to the boil and stir until smooth and emulsified. Pass through a fine sieve and cool.
7: To construct and finish the tarts, trim the excess pastry from the tops with a small, sharp knife and remove them from the tins. Spoon in a generous portion of the crème patissière. Place the strawberries in a ring around the top of the tarts, trying to ensure the slices overlap neatly, then brush the strawberries with the glaze. Place a lovely scoop of strawberry ice cream in the centre of each and decorate with a few baby basil sprigs. Serve immediately.