Preheat oven to 180 C / Gas 4. Grease and flour one 26 to 28 cm round cake tin.
Prepare plums and sprinkle with juice of 1/2 lemon. Set aside.
Add butter, sugar, flour, eggs, soured cream, baking powder, salt and lemon zest to food processor. Mix until smooth. Transfer to prepared tin.
Arrange plums on top of cake mixture, cut-side down. Plums can touch or even overlap. The more you can fit, the better! Dust with cinnamon.
Bake in preheated oven for 45 to 50 minutes, or until a skewer inserted in the centre comes out clean. Cool 15 to 20 minutes before serving. Dust with icing sugar if desired.
If mixing by hand:
Cream softened butter and sugar together, add eggs one at a time, then the lemon zest. Then add the flour (sifted together with baking powder and salt) alternately with the soured cream, adding a little at a time. Mix until light and smooth.
I usually soften butter in microwave for 12 to 15 seconds (exact time will depend on your microwave).