Preheat the oven to 170°C and grease and line a deep 15cm round tin.
Beat the butter, sugar, and vanilla in a bowl until pale and fluffy.
Add eggs one at a time, beating after each addition.
Mix the yogurt with food coloring until it is very red.
Beat the red yogurt mixture into the cake batter.
Fold in the flour and cocoa powder followed by the milk.
Spoon mixture into the tin and bake for 80 minutes until golden.
Cool the cake in the tin for five minutes before moving to a wire rack.
Mix butter and cream cheese together for the icing.
Gradually beat in the icing sugar followed by the lemon juice.
Slice the cooled cake into three layers and assemble with icing between and on top.