Preheat your oven to 350°F (175°C) and grease or line an 8-inch round or square baking pan with parchment paper.

1. Prepare the cake base: In a medium bowl, whisk together the flour, baking powder, and salt. Set aside. In a large bowl, beat the softened butter and sugar together until light and fluffy. Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract. Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the dry ingredients. Mix until just combined.
2. Pour the cake batter into the prepared pan, spreading it evenly across the bottom.
3. Make the custard filling: In a saucepan, combine the heavy cream, milk, and sugar over medium heat. Stir until the sugar dissolves and the mixture is heated through, but not boiling. In a separate bowl, whisk the egg yolks and cornstarch until smooth. Slowly pour in the hot cream mixture, whisking constantly to avoid curdling.
4. Return the custard mixture to the saucepan and cook over medium heat, stirring constantly, until the custard thickens and coats the back of a spoon (about 5-7 minutes). Remove from heat and stir in the vanilla extract.
5. Pour the custard over the cake batter in the pan, spreading it evenly.
6. Gently press the raspberries into the custard, evenly distributing them over the surface.
7. Bake for 35-40 minutes, or until the custard is set, the top is golden, and the cake is cooked through. You can test this by inserting a toothpick into the cake portion, which should come out clean.
8. Allow the Kuchen to cool for 15 minutes before transferring it to a wire rack to cool completely.
9. Once cooled, dust with powdered sugar if desired, and slice into squares or wedges. Serve chilled or at room temperature.