Heat a griddle pan to medium high. Brush the burgers with the oil and then add to the pan. Cook for 5-6 minutes before turning over and cooking for a further 5-6 minutes, or until cooked through. Divide the stilton between them and pop under a hot grill for 1-2 minutes until the cheese is melted. Remove from the grill and leave to rest for 5 minutes.
Meanwhile, slice the burger buns in half and add to the hot griddle pan, toasting on each side for 30-45 seconds each or until they start to colour. You might need to do this in two batches, depending on the size of your pan.
Fill your burger buns with the lettuce, burgers and the tomato. Serve.