With a mixer, first blend the sugar and butter then add the lemon zest, the eggs, and at the end, flour and baking powder. Carefully wash the plums keeping the skins and cut them in half removing the seed with a knife. Line a large, round 25 cm pan with parchment paper, pour the cake mix into the pan and, place the plum halves, cut side down, on top of the cake mix; sprinkle sugar over the top. Bake in the oven for 45 minutes at 170°C or 330°F.