Preheat the oven to 200°F. Place the ham in an oven safe pan or dish. Cover with foil and warm in oven while you cook the eggs and ham.
Melt the butter in a medium saucepan over medium heat and whisk in the flour. Return to heat and gradually add the milk whisking frequently until smooth. Turn off heat and add the cheese, salt and pepper to taste and blend until cheese is melted.
In a non-stick skillet drizzle a little oil and gently bring to a medium heat. As the pan is heating crack 4 eggs into 4 ramekins or small bowls. When skillet is ready place 4 pepper rings in skillet. Gently tip an egg into each ring. Fry for 2 – 3 minutes, for sunny side up with a runny yolk. Longer if you prefer a medium textured yolk.
Place a piece of toast to a serving place. Add two slices of ham on top of bread and cover with an egg ring. Spoon some cheese sauce on top. Garnish with some chopped scallions, if desired.