Heat a panini or sandwich press according to the manufacturer's instructions. (Or, cook the panini in a grill pan or skillet over medium-high and use another heavy pan or skillet to weigh the sandwich down as it cooks, turning to brown both sides.)

In a small bowl whisk together the lemon juice, zest, olive oil, mayonnaise, tuna juices and a pinch of salt and pepper. In larger bowl add the tuna and break it up with a fork, then add the onion, capers, parsley and mayonnaise mixture. Stir to combine well, mashing to smooth out any large chunks. Taste and add more salt, pepper or lemon as needed.

Arrange the tuna on top of two of the bread slices. Top with the cheese followed by the remaining bread slices. Put the sandwiches on the press, pull the top down, and cook until they are browned and crisp, 3 to 6 minutes, depending on how hot your machine is. Carefully remove from the press, cut into halves or quarters and serve immediately.

Makes 2 sandwiches.