Heat oven to 350°F. Line the bottom of an 8-inch round cake pan with parchment paper. Butter and flour the pan. Beat the butter and sugar together at medium-high speed until fluffy. Beat in the eggs and yolks, one at a time, and add the vanilla extract. Stir the cake flour, baking powder, and salt together using a whisk. Reduce mixer speed to low and beat the flour mixture into the butter-egg mixture, adding it in thirds and alternating with the milk. Beat until the batter is smooth. Transfer to the prepared pan and bake on the center shelf of the oven until the cake tests clean when a skewer is inserted into the center, 35 to 40 minutes. Cool completely on a wire rack. To assemble, split the unmolded cake using a long serrated knife. Spread Vanilla Bean Pudding over the bottom half of the cake and place the top layer over the pudding. Pour Chocolate Glaze over the cake, allowing it to drip down the sides of the cake.