Brush one side of each slice of bread with olive oil.
Build the sandwiches on two of the slices, layering the ingredients equally in this order:
a sprinkling of cheese, avocado slices, pear slices, fig jam, arugula, the rest of the cheese, and the top slice of bread.
If using a panini press, brush the outsides of the bread with olive oil and heat the press and grill the sandwiches as directed.
If using a griddle, heat over medium heat; when hot, add two tablespoons of olive oil in two separate pools and place a sandwich over each pool.
Press down on the sandwiches with a large spatula.
When the bottoms have browned, flip the sandwiches and repeat.