Stir the tuna, mayonnaise, red onion, lemon juice, and oregano together in a medium bowl, then season with salt and pepper to taste. The mixture should look creamy and evenly combined, but not overly wet or soupy, so add more mayo only if it seems too dry.

Butter the outsides of the bread, then pile the tuna mixture onto the unbuttered sides and add cheese, any optional avocado or tomato, another slice of cheese, and the top bread slices. Placing cheese on both sides helps keep the filling tucked in and gives you a better melt through the center.

Set the sandwiches in a skillet over medium-low heat and cook until the first side is toasted and the cheese starts to soften, then flip and finish the second side until the bread is crisp and the cheese is melted. You’re looking for a deep golden brown crust that sounds lightly crisp when cut, with gooey cheese all the way through.