Place bread on a work surface and spread mayonnaise evenly on one side of each bread slice.

Toss havarti cheese and chopped dill pickles together in a bowl until evenly combined.

Divide the cheese mixture evenly among 4 bread slices. Place remaining 4 bread slices, mayonnaise side down, on top to assemble the sandwiches.

Spread half of the softened butter evenly over the tops of the sandwiches. Heat a large skillet over medium heat.

Place sandwiches in the skillet, buttered side down. Spread remaining butter onto the tops of the sandwiches.

Cook until the bottom side is golden brown and toasted, about 4 minutes. Flip the sandwiches and cook until cheese is melted and the bread is golden on both sides, about 4 minutes.