In a medium mixing bowl, add ketchup and mayonnaise. Stir with a fork until both sauces are fully integrated.
Place the bread slices on a cutting board, arranged in stacks of no more than four slices. Cut the dark edges with a bread knife. Repeat with all slices of bread.
Next, take all the bread slices and spread them on one side with a thin layer of pink sauce.
On a slice of bread place, a slice of cheese, and a slice of ham. Top with another slice of bread. The part of the bread that has sauce should be on the inside. Repeat this procedure with all the pieces of bread, until making 5 sandwiches.
Place the sandwiches, two at a time, on the grill pan. Cook for most of three minutes on each side. Until the cheese melts.
Then put the toasted sandwiches on a cutting board, and cut them into two or four pieces, to your liking. We cut them in two because our slices of bread are not very big.
Put a piece of sandwich on a plate, add a piece of lettuce on top, and cover with another piece of bread. Hold everything down with a wooden toothpick. Serve with more pink sauce.