Heat a dash of oil in a frying pan. Sauté the carrots and leek for approx. 2 mins., allow to cool a little. Mix the vegetables and oat flakes in a bowl. Add the eggs and salt, knead by hand to form a compact mass. Divide the mixture into 4 portions, shape into 4 burgers, flatten a little. Heat the oil in the same pan. Reduce the heat, fry the burgers over a medium heat for approx. 4 mins., turn. Place one slice of cheese on each burger, cover and continue to cook for approx. 4 mins., remove.
Toast the bread rolls in the same pan, cut side down, remove. Place the lettuce leaves on the bottom half of the bread rolls. Mix the strips of beetroot with the BBQ sauce, arrange on top of the salad. Place a burger and slice of cucumber on top. Cover with the top half of the roll, using toothpicks secure two olives as eyes.