Warm 250 ml milk in a 2-quart / 1.9 L saucepan over medium heat until steaming, about 3 minutes. Whisk the 2 egg yolks, 40 g sugar and 2 tbsp cornstarch in a bowl until smooth, then pour in the hot milk in a slow stream while whisking.

Pour the mixture back into the saucepan and cook over medium heat, whisking constantly, for 2 to 3 minutes until it bubbles. Keep whisking for 1 more minute until it holds a ribbon on the whisk. Off the heat, stir in 1 tsp vanilla and 15 g butter. Press plastic wrap onto the surface and cool until lukewarm, about 20 minutes, while you make the cake.

Heat the oven to 175 C / 350 F. Grease a 23 cm / 9-inch springform pan and line the base with parchment. For the crumble, mix 100 g flour, 50 g brown sugar and a pinch of salt, then rub in 60 g cold butter with your fingertips until you have pea-sized clumps. Chill it in the fridge.

Beat 115 g softened butter with 130 g sugar for 3 minutes until pale and fluffy. Beat in the eggs one at a time, then 1 tsp vanilla. Fold in the flour, baking powder and salt in two additions, alternating with the milk, until no dry streaks remain. Scrape the thick batter into the pan and smooth the top.

Spread the lukewarm custard over the batter, leaving a 1 cm border at the edge. Toss the gooseberries with 30 g sugar and 1 tsp cornstarch, then scatter them over the custard in a single layer.

Squeeze the crumble into clumps and scatter it over the fruit. Bake on the middle rack for 55 minutes, until the crumble is deep golden and the center barely moves when you nudge the pan.

Cool the cake in the pan for 15 minutes. Run a knife around the edge, release the ring, and move the cake to a wire rack for 30 minutes more before slicing. The custard sets as it cools.