The apples in this vanilla-scented cake explain the pudding's name and tempting qualities.
Preheat oven to 350 degrees. Butter an 8 1/2-inch square baking dish; set aside. Whisk flour, baking powder, and 1/2 teaspoon salt in a medium bowl; set aside.
Put apples, 1/4 cup sugar, the lemon juice, cinnamon, and a pinch of salt into a large bowl; toss to combine. Transfer to prepared baking dish, and sprinkle 2 tablespoons water over top; set aside.
Put butter and 6 tablespoons sugar into the bowl of an electric mixer fitted with the paddle attachment. Mix on medium-high speed until pale and fluffy. Add eggs, one at a time, mixing after each addition. Mix in vanilla. Reduce speed to low. Add flour mixture, alternating with milk. Mix until combined.
Spread batter over apples, and sprinkle with remaining 2 tablespoons sugar. Bake until batter is cooked through and juices are bubbling, about 40 minutes. Let cool on a wire rack 15 minutes. Spoon into dishes; serve drizzled with cream.