APPLES: Preheat the oven to 350 degrees. Line the bottom of a 9-inch round cake pan with parchment paper. In a medium bowl, combine butter, brown sugar, cinnamon and salt. Spread the mixture evenly in parchment lined cake pan. Arrange the apples wedges over the mixture in 2 concentric circles.
CAKE: In a large bowl, whisk the flour, 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.
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 cake and plate. Remove the pan and peel off the parchment paper. Let the cake cool completely.
GLAZE: In a small bowl, stir the confectioners' sugar with the milk and drizzle it over cake. Cut into wedges and serve.