Grease a 1.5 litre pudding basin with butter.
Melt butter, sugar, and vanilla in a pan until caramelised.
Stir in cream, simmer until reduced slightly, and cool completely.
Fry apple pieces in butter for 3-4 minutes until caramelised and tender.
Beat butter and sugar together until pale and fluffy.
Gradually incorporate beaten eggs into the butter mixture.
Mix in the flour until the sponge batter is well combined.
Layer apples, most of the sauce, and batter into the basin.
Cover with pleated parchment and foil, then secure with string.
Steam in a water bath for 1.5 hours, topping up water levels.
Boil milk, cream, and vanilla, then infuse for 15 minutes.
Whisk egg yolks and sugar, then combine with the warm milk.
Strain and cook over low heat until the custard coats a spoon.
Serve pudding slices drizzled with remaining sauce and crème anglaise.