Bolzano Apple Cake

Directions

1. 1
   Heat oven to 375 degrees. Line 8-inch square pan with foil, then smear with thick layer of butter. Dust with flour; turn pan over and tap lightly to remove excess flour.
2. 2
   Melt butter in small saucepan. Set aside. Beat together eggs and half the sugar in a bowl. Continue to beat while slowly adding remaining sugar until thick; it should form a ribbon when dropped from a spoon.
3. 3
   Split vanilla bean in two lengthwise. Scrape seeds into egg-sugar batter and add pod to melted butter.
4. 4
   Peel, quarter and core apples, then trim ends and slice thinly.
5. 5
   Remove vanilla pod from butter and stir butter into egg-sugar batter. Combine 1/2 cup flour and baking powder, then stir it into batter alternately with milk. Stir in apples, coating every piece with batter. Pour batter into pan, using fingers to pat top evenly.
6. 6
   Bake for 25 minutes, then rotate pan; bake for about 25 minutes more, until cake pulls away from pan and is brown on top; a thin-bladed knife inserted into center will come out clean when it is done. Cool 30 minutes, then cut lengthwise and sprinkle slices with powdered sugar.