Preheat a large nonstick skillet over medium heat for 2 minutes. Add the salami and cook until it begins to brown, 2 to 3 minutes. Turn and cook for about 3 minutes, or until the slices have begun to shrink and turn golden brown. Transfer the salami to a plate. Wipe the skillet with a paper towel, but do not wash it.

To assemble: Brush one side of each slice of bread with the oil. Place 4 slices on your work surface, oiled side down. Distribute the cheese evenly over the 4 slices, followed by the salami. Place the remaining 4 bread slices on top, oiled side up.

STOVETOP METHOD: Heat the same skillet over medium-high heat for 2 minutes. Put the sandwiches in the skillet (in batches if necessary), cover, and cook for 2 minutes, or until the undersides are golden brown and the cheese has begun to melt. Uncover, and turn the sandwiches with a spatula, pressing firmly to flatten them slightly. Cook for 1 minute, or until the undersides are golden brown. Turn the sandwiches again, press with the spatula, and cook for 30 seconds, or until the cheese has melted completely. Serve immediately.

SANDWICH MAKER METHOD: Preheat the sandwich maker. Follow directions for sandwich assembly, and cook according to the manufacturer's instructions.

GAS GRILL METHOD: Brush the grill rack with oil and preheat the grill to medium-high. Follow directions for sandwich assembly. Put the sandwiches on the grill and follow directions for the stovetop method.