To make pastry cream: In a saucepan, combine the milk and 5 tablespoons sugar. Bring to the boil, stirring to dissolve sugar. Remove from heat. In a small bowl, combine an additional 5 tablespoons sugar and 2 tablespoons flour. Beat in the eggs and vanilla.
Mix 125ml of hot milk into egg mixture, then pour the egg mixture back into the saucepan with the hot milk. Return to heat and bring to the boil. Continue cooking over medium heat until mixture thickens and becomes smooth. Remove from heat and let cool for 1 hour.
Preheat oven to 180 C / Gas 4. Grease and flour a 23cm round springform tin. Combine and sieve the flour and baking powder together. Set aside
Cream 225g sugar and 3 eggs until light and fluffy. Fold in the flour mixture in three increments, being careful not to overmix.
Transfer half of the mixture into the prepared tin. Spread so that it covers the bottom of the tin. Place pastry cream to within 1.75cm of the edge. Add the second half of the cake mixture making sure to enclose all of the filling.
Bake at 180 C / Gas 4 for 30 to 40 minutes or until golden brown.