Preheat a Panini press, sandwich press, or a pan over medium heat.
Set out the four slices of bread and spread one side of each with mayonnaise. Place two slices of bread mayo side down onto your preheated grill or pan and top with half of the cheese, the prosciutto, pears, and remaining half of cheese.
Drizzle with honey, spread Dijon onto the bare side of the remaining two slices of bread, and pop them on top of the sandwiches, mayo side up.
Cook until the bottoms are golden brown and the cheese is starting to melt, about four minutes.
Flip and cook the other side until golden and the cheese is fully melted. Cut each sandwich in half and serve immediately.