In a skillet over medium-low heat, cook onion with butter covered for 13-15 minutes until tender. Uncover and cook over medium heat for 3-5 minutes until golden and caramelized. Set aside.

In a bowl, mix the mayo and bbq sauce together until smooth. Set aside.

On the outside side of each slice of bread, spread with softened butter.

To make each sandwich, place one slice of bread butter side down in a skillet, spread the facing side up with the bbq mayo. The top with 1-2 pieces of cheese, 1/4 of the ham, a couple slices of tomato, and 1/4 of the caramelized onions. Take anther slice of bread, spread the non-butter side of the slice with the bbq may and place bbq mayo side down on the sandwich. Cook each side of the sandwich over medium heat until golden on both sides.

Repeat the process with the remaining ingredients to make 3 more sandwiches. Makes 4 sandwiches.