In a large bowl, use a fork to mash up the tuna completely - no big chunks should remain. Dice the pickles and add them to the bowl, along with the mayonnaise, salt, and a few grinds of pepper.
Lay out 4 slices of the bread on your countertop and place a slice of cheddar cheese on top. Spoon your desired amount of tuna salad onto each, then top with a second slice of cheddar.
Warm your largest skillet (or griddle if you have one!) over medium heat for 3 to 4 minutes. Top the sandwiches with the remaining 4 slices of bread. Spread a thin layer of mayo over the tops of the sandwiches, then sprinkle with half the Parmesan, pressing to adhere. Working in batches as needed, gently place the sandwiches, Parm-side down, into the skillet.
Cook the sandwiches, pressing down gently every once in a while with a spatula, until the bottoms are toasty and crispy and the bottom slice of cheddar has melted, 3 to 5 minutes.
Carefully flip the sandwiches and cook until toasty and crispy and melty on the second side, 2 minutes or so more.
Transfer the sandwiches to a cutting board and let them rest for a few minutes; if you cut right in, everything will just ooze out. When it's time, slice your melts in half and enjoy.
