In a small bowl, combine the Gouda, salami, and artichoke hearts. Divide the mixture between 2 slices of bread, spreading evenly to cover bread. Top with remaining bread slices and gently press together to seal in filling.
In skillet, melt 1 T. butter over medium heat. Cook sandwiches for 1 minute or until golden. Remove and add 1 T. butter.
Flip sandwiches and cook for 1 minute more, or until golden, pressing with spaulta slightly.