The mozzarella and tomato panini is defined by water, and the press is what forces the issue. Mozzarella is a wet cheese that holds moisture even as it melts; tomato is mostly water held in a structure that bursts under heat. Clamp the two together in a roll between hot ridged plates and the panini either resolves into a molten, just-set centre against a crisp shell, or it floods, the tomato weeping into the crumb and the mozzarella sliding out the open sides as it goes liquid. The defining craft is controlling that water so the heat melts and fuses the filling without turning the bread to a soaked, collapsing base.
The craft is drainage and arrangement. The mozzarella is used drier than it comes, blotted or left to lose some moisture, and a firmer block type holds the press better than the softest fresh balls, which go to liquid and run. The tomato is sliced and salted or drained, or used as a thicker sun-dried or roasted form that has already lost its water, and it is kept off the cut faces of the roll, with the cheese as a partial seal between it and the bread so the crumb is not soaked from the centre out. The roll is a close, firm-crumbed one that crisps under the clamp rather than crushing flat, and the build is filled and pressed to order, because the contrast that defines it, brittle grilled shell against a soft molten interior, exists only in the minutes after pressing and is gone once it cools and the cheese sets rubbery.
The variations stay inside the melt-against-water frame. Basil added after pressing keeps a fresh note heat would blacken; a smear of pesto turns it toward the chicken-and-pesto build's oily logic. Roasted vegetables, red pepper, or olive tapenade push it Mediterranean while keeping the moisture under control. A buffalo mozzarella version leans richer and wetter and demands harder draining to survive the press. The chicken and pesto panini solves the opposite problem, a filling too dry rather than too wet. Each deserves its own article rather than being crowded in here.