Spread 1 tablespoon of softened butter on two slices of bread. Flip one slice over and spread un-buttered side with 2 tablespoons fig preserves. Layer with one slice of Havarti (or 1/8 cup shredded), half of the ham, and top with one more slice of Havarti (or 1/8 cup shredded). Place remaining slice of bread on top, buttered side up.

Melt 2 tablespoons butter in a skillet over medium heat. Add sandwich and allow to cook until nicely browned on one side. Use a spatula to carefully flip the sandwich and allow to cook until browned and cheese has melted. If necessary, remove pan from the heat and place cover on for a minute or two until cheese has completely melted.

Repeat with remaining ingredients to make second sandwich. Serve warm.