Making the Panini without a Panini Press: Preheat a grill pan or a frying pan/skillet over medium heat until the pan is hot (about 1 minute). Then, add the panini to the pan and press with a heavy object, such as a large cooking pot or another heavy pan. Cook the panini over medium heat (keeping them pressed) for about 3 minutes per side (until you can see the cheese has melted).