Brush the sandwich toaster with a little sunflower oil and preheat to its highest setting.
Brush the bread with oil on one side only. Break the eggs into two separate cups.
Place one slice of bread in the toaster (oiled side down) and press the bread down into the triangular recesses with the back of a spoon (taking care not to puncture the bread or your egg will leak out). With a metal spoon, carefully spoon the whole yolk of each egg into each of the two recesses. Whisk the white of the eggs lightly with a fork to break them up a bit and then spoon as much white around the yolks as your recess will hold. Do not overfill or your sandwich will leak. You may well have some egg white left over; as a guide, I can get about 1.5 egg whites in my toaster.
Gently place the second slice of bread on top (oiled side up) and bring the lid down slowly so that it rests on the sandwich. (Do not squash it or attempt to lock the toaster shut at this stage). Leave in this position for 2 minutes. Then, slowly close and lock the lid, and cook for a further 3 minutes. After this time the toastie should be golden and crisp on the outside, and on the inside the white should be set and the yolk still runny.