Whisk together the eggs and milk in a medium bowl. Set aside.
Add about 1/2 tablespoon butter to a large sauté pan. Heat to medium.
Add two slices of bread and heat until toasted. Add another 1/2 tablespoon of butter, flip the bread and toast the other side. Remove to a plate.
Repeat with the remaining two slices of bread.
Heat another tablespoon of butter in the pan. Add the ham, bell pepper and onion, and sauté a couple of minutes- until softened.
Add the egg mixture and sprinkle cheese on top. Sprinkle salt and pepper. Let the eggs cook until lightly browned underneath.
Then take a rubber spatula and drag them around until cooked all the way through. Remove from heat.
Assemble the sandwiches- divide the egg mixture between two slices of bread. Add ketchup, if desired. Top with the other piece of bread, slice in half and enjoy!