If you are using uncooked gammon steaks, pan fry until cooked.
Place the potatoes in a large pot of water and bring to a boil. Turn the heat down and simmer, covered, for 10 minutes. Add in the carrots and continue to simmer for another 5 minutes. Add in the eggs and continue to simmer for 10 minutes. Drain the water and allow everything to cool until you can handle it.
Cut the potatoes into 1/2-inch pieces. Cut the cooked gammon steaks, carrots and celery into 1/4-inch pieces. Peel the eggs and roughly chop (including the egg yolk, which will crumble) into small pieces. Add everything into a large bowl.
In a small bowl, mix the mayonnaise, salt, and pepper together (it is easier to mix it all the seasoning together first before adding it to the potato salad).
Add the mayonnaise mixture over the salad and mix until well combined.
Refrigerate for at least 4 hours before serving. To serve, generously sandwich the potato salad between two slices of white bread.