Prepare a 9-inch springform pan by lining the bottom with parchment (I basically cut a large square of paper, place it on the base, then clip the sides over so that the paper runs right through the springform). Butter the paper and the sides of the springform pan. Wrap the outside of the pan with 2 large sheets of aluminum foil (in case your springform is as leaky as mine is). Set aside.
Make the quick caramel sauce
In a small saucepan, melt the butter and brown sugar until it gets bubbly. Let it bubble for about 2 minutes, stirring constantly.
Pull the pan off the heat and pour the mixture into the bottom of the prepared pan. Smooth it out so that it forms an even layer. Set aside.
Prepare the fruit
In a medium bowl, combine the fruit with the granulated sugar and cornstarch. Mix it carefully to not damage the raspberries too much, and let it sit. Stir the fruit every few minutes to evenly distribute the starch and sugar.
Make the cake batter
Whisk together the flour, ground almonds, baking powder, and salt in a medium bowl. Set them aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream the butter and the granulated sugar.
Add the vanilla, and then the eggs, one at a time, beating well, and scraping down the sides of the bowl after each addition. Don’t worry if the batter looks curdled at this point.
Alternately, add the dry ingredients (one-third at a time) and the yoghurt (half at a time), beginning and ending with the dry ingredients. Be sure to scrape down the sides and the bottom of the bowl occasionally.
Assemble the upside-down cake and bake
Arrange the fruits evenly on top of the sugar layer (either decoratively or just neatly arrange them to fit snuggly). Pour the juices over the fruit.
Dollop the cake batter carefully over the fruit being sure to smooth the top without disturbing the fruit layer. Bang the pan on the counter so as to remove any air pockets (you could also swirl a knife through carefully to remove any air pockets, just be sure to avoid the fruits at the bottom).
Bake for 1 hour 40 minutes to 1 hour 50 minutes, until a cake tester inserted into the centre of the cake comes out clean. Because the cake is tall, it takes a long time to bake the middle so make sure you bake it for long enough!
Let the cake cool for 15 minutes in the pan, then place your serving plate over top, and flip it very carefully because the fruit juices are boiling hot! Set the plate on a wire rack to cool completely. Do not let the cake cool in the pan because the fruits and juices will stick to the bottom, and you’ll have a hard time getting it out after.