Split each roll, and layer with the mozzarella and prosciutto.
Spread the top slices with the fig jam, then close up to form sandwiches.
Lightly butter the outside of each sandwich.
Heat a heavy nonstick skillet or panini press over med-high heat.
Place the sandwiches in the pan, working in two batches depending on the size of the pan.
Press the sandwiches or close the grill and brown, turning once or twice, until the bread is crisp and the cheese is melted; **you can press the sandwiches by weighting them with something heavy—such as a skillet or wide-bottomed saucepan.
Though the rolls start off as round, once pressed they are considerably flatter and can easily be turned, if careful.