Preheat the oven to 400˚F. Grease a 9-inch springform pan.
To make the cake, whisk together flour, sugar, baking powder, salt, and mace. Add the butter and cut into the flour mixture until it resembles coarse meal. In another small bowl, whisk together milk and egg. Pour it to the flour mixture and combine well.
Spread the batter into a prepared pan and arrange the apricot slices on top. Bake the cake for 15 minutes.
To make the custard, combine 1/4 cups of cream with flour in a medium mixing bowl, and whisk together to get rid of big lumps. Add the rest of the cream, sugar, egg, and vanilla; whisk well to mix.
When the cake comes out of oven, pour the custard mixture into hot cake and put it back to the oven. Reduce the heat to 350˚F and continue to bake for another 35-45 minutes.
When the cake top is puffed, the edges are deep golden and starting to separate from the pan, the cake is done. Let the cake cool in a pan for 10 minutes. Remove the cake ring and cool completely on a wired rack.