Add the egg and mustard to your food processor, and blend this until mixed.
While the machine is running, you can pour in the olive oil (very slowly) in a thin stream.
When all the olive oil is incorporated, you can add the vinegar and mix again.
Then while the machine is on, you can slowly pour in the sunflower oil, salt & pepper.
*When your mayonnaise is curdled, you can add an extra egg yolk. Mix the mayonnaise again, and it will be good to go again!