Preheat the oven to 175 °C (350 °F) top/bottom heat. Grease the springform pan or line it with parchment paper.
For the frangipane, cream the soft butter with the sugar. Add the egg, ground almonds, flour, and vanilla, and mix into a firm, pipeable cream. Fill into a piping bag and chill briefly so it becomes nice and stable.
For the cake batter, beat the soft butter with the sugar until light and creamy. Mix in the eggs one at a time. Combine the flour with the baking powder and stir in alternately with the milk and vanilla until you have a smooth batter.
Pour the cake batter into the pan and smooth the top.
Pipe the frangipane on top in thick lines. If some is left, pipe a second layer on top - nice and thick.
Sprinkle with sliced almonds.
Bake for about 40-45 minutes, until the cake is golden brown and baked through (toothpick test in the cake batter part).
Let cool slightly, remove from the pan, and dust with powdered sugar.
