Set aside 2 pieces of bread for each sandwich. To assemble, spread 1 tablespoon mustard on one slice of bread, and 1 tablespoon mayonnaise on the other.
Place 2 ounces turkey, 4 pear slices, 1/4 cup arugula and 2 ounces cheese on one slice of bread and top with the other. Press down slightly on the top slice of bread and lightly brush it with olive oil.
Place the sandwich, oiled side down, on a hot griddle or panini press. If using a griddle, weigh the sandwich down with a griddle or steak weight, or a foil-wrapped brick. Grill 2 minutes, remove the weight and lightly oil the side facing up, then flip the sandwich over and grill another 2 minutes or until the cheese melts, the meat is heated through and the bread is golden brown.
Remove the sandwich from the griddle or press, slice on the diagonal and serve immediately.