Soak the tapioca in cold water for 2 hours; then mix it with the sugar, milk, eggs and vanilla extract; pare and core the apples, put them in a pan with water, cover them with another tin pan and let them boil 5 minutes; remove the apples carefully, put them into a pudding dish, pour the tapioca mixture over them and bake in the oven; serve with hard sauce or send it to table without sauce sprinkled with powdered sugar.