Lightly spread olive oil on panini press and on outer side of both slices of bread. Spread Dijon mustard over inside of one of the slices. Sprinkle 2 tbsp. of the Gruyere over one slice of bread, oil-side down. Top with the slices of ham. Sprinkle about 1 tbsp. green onions over the ham, followed by the remaining 1/4 cup of Gruyere. Top with remaining slice of bread, oil-side up.