How to Make It
Preheat the oven to 350° and line the bottom of a 9-inch cake pan with parchment paper. In a large bowl, blend the butter with the brown sugar and salt. Spread the mixture evenly in the lined cake pan. Arrange the apples wedges in the pan in 2 concentric circles.
In the same bowl, whisk the flour with the sugar, baking powder and salt. In a small bowl, mix the eggs with the milk and vanilla. Add the mixture to the dry ingredients along with the melted butter and whisk until smooth. Scrape the batter over the apples and spread evenly. Bake the cake in the lower third of the oven until golden and springy and a toothpick inserted in the center comes out clean, about 1 hour and 15 minutes.
Transfer the pan to a rack and let cool for 30 minutes. Run the tip of a knife around the inside rim of the pan. Center a serving plate over the cake; carefully invert the the cake and plate. Remove the pan and peel off the parchment paper. Let the cake cool completely.
In a small bowl, stir the confectioners' sugar with the milk and drizzle it over the cake. Cut into wedges and serve.