Heat a skillet large enough to fit one slice of bread over medium low heat.
Butter one side of one slice of bread and place it butter side down in the hot skillet. Top the bread with half the cheese, the sliced avocado, giardiniera, and the remaining cheese. Butter one side of the remaining slice of bread and place it on top with the butter facing up.
Heat until golden brown on the bottom, then flip carefully and cook the other side until golden brown. If it seems like the cheese isn’t completely melted yet, lower the heat and continue to cook, flipping frequently, until everything is hot and melted.
Let the sandwich rest for a minute before cutting it in half and enjoying it.