Carefully cut the green olives into 1.5cm-wide discs. Slice small circles from the black olives to fit inside the green olive discs.
Use the tomato purée to stick each green olive on to a mozzarella pearl, then attach the black olives on top of the green olives with a little more tomato purée if needed. Use a thin piping nozzle to pipe wriggly tomato purée lines all over the mozzarella.
Transfer to a lined baking tray and chill in the fridge for 30 minutes before serving.