1. Halve the fruit and remove the pits. Slice the fruit into 3/4- to 1-inch (2-3cm) wedges. Set aside. Preheat the oven to 350ºF (180ºC.) Grease a 9-inch (23cm) springform pan very well with butter or non-stick spray. (If you don’t have a springform pan, you can use another cake pan but it may be harder to get the cake out so you may want to also line the bottom with parchment paper.)
2. In a medium mixing bowl, stir together the almond flour, all-purpose flour, baking powder, salt, and sugar. (My preferred tool to use for this step is a silicone spatula.) Add the soft butter and mix it in with the spatula until it’s broken up into little pieces, roughly the size of kernels of corn. Stir in the eggs and vanilla extract, until it’s almost smooth. It’s fine if there are small pieces of butter visible.
3. Scrape the batter into the prepared pan and smooth the top. Arrange the wedges of fruit on their sides in concentric circles over the batter, snugly placing the wedges against each other, pressing them gently into the batter as you go. Avoid putting them right up against the sides of the pan. It’s best to leave some room for the batter to rise between the fruit and the pan, to avoid juices from the fruit adhering to the sides of the pan as the moelleux bakes. (It’s unavoidable – and natural – if using juicy fruits, like plums, to have juice run out. But placing the slices not right up against the sides of the pan will help you get the cake out of the pan later.)
4. Sprinkle the coarse sugar over the top and bake until the center just feels set; a toothpick inserted into the center should come out free of cake crumbs stuck to it, about 1 hour. Remove from the oven and set on a cooling rack. If any fruit juices have bubbled up and stuck to the sides of the pan, run a knife around the outside of the cake, which will help it release later.