In a small bowl, combine cheeses. Spread the cheese on the bottoms of the ciabatta rolls. Top with tomato slices and brush with olive oil. Sprinkle with basil and add 2 arugula leaves and close the panini.
Set a large cast-iron skillet or griddle over moderately high heat. Arrange the panini in skillet and weight them down with a smaller pan (can fill with water if you need more weight). Cook the panini until the outside is crisp and the cheese is melted, 3 minutes per side.