Preheat the oven to 350 degrees F.
Cut the plums into quarters, leaving the edges of the skin attached so that the quarters remain connected after removing the pit.
Mix together the flour, sugar, lemon juice, baking powder, butter and egg in a large bowl with a wooden spoon, and then knead with your hands to form a dough.
Press the dough down into a round cake pan with your fingers to form an even crust. Combine the granulated sugar and the cinnamon in a small cup and sprinkle some of the mixture on the dough.
Layer the rows of prune quarters over the dough with the flesh facing upwards until the entire crust is covered. Sprinkle with some brown sugar. Bake the cake for 1 hour 30 minutes.