Place griddle pan over medium heat.
Spread a thin layer of pesto on one slice of bread. Add cheese, and top with other slice of bread.
Add butter to hot pan. Melt and spread around to cover an area big enough for the bread.
Sprinkle parmesan and a small amount of garlic salt on the melted butter.
Place sandwich on the pan, sliding it around to pick up all the flavors.
Once the bottom side is browned remove the sandwich and place on a plate.
Repeat the butter, parmesan, and garlic salt on the pan. Place sandwich on the other side to brown.
Cook until both sides are browned and cheese is melted.