Fill a small pot two-thirds full with water and bring to a boil.
2. Step
With a paring knife, poke a small hole into the wider end of the egg. With a spoon, gently lower eggs into the boiling water and boil for precisely 5 minutes.
3. Step
Cut the cheddar cheese into strips, 4 inches (10 cm) long, ¼ inch (½ cm) thick.
4. Step
Roll out a piece of white bread until flat and dense.
5. Step
Place a slice of ham on the bread, then top with a strip of cheddar. Roll up the bread (like a jelly roll) until cheese and ham are entirely covered.
6. Step
Fry the bread rolls for about 4 minutes in a buttered sauté pan over medium-high heat. Turn halfway through when rolls are lightly browned.
7. Step
When eggs are done, carefully transfer them to a bowl of ice water.
8. Step
Meanwhile, use an egg carton to cut out egg holders for each egg.
9. Step
Take eggs out of ice water. Serve with the ham and cheese dunkers.
