Mix the meat with all the other ingredients up to and including the salt, knead well by hand until the ingredients have combined to form a compact mass. With wet hands, shape the mixture into 4 burgers, flatten a little.
Charcoal/gas/electric grill: Grill over/on a medium heat (approx. 200 °C for approx. 6 mins. on each side.
Combine the crème fraîche and tomato puree, season.
Grill the burger buns (cut side down) over a medium heat (approx. 200 °C for approx. 1 min. Spread 1 tbsp of sauce on each, top with 1 lettuce leaf and 1 burger. Place 2 slices of egg on the top half of the meat for the eyes, place 2 olive rings on top for the pupils. Use 1 tomato half for the nose and 1 slice of cucumber for the mouth. Add a little cress for the hair.