Spread one side of each of the four slices of bread with an equal amount of the softened butter. Place two slices on a cutting board, butter side down (a bit messy, yes), and layer sprinkle half of each type of grated cheese on the bread. Spread the other two slices with the jam. Top the sandwiches with the jam-spread two slices bread, butter side up.
Heat a large pan with a lid (either nonstick, or one that has been sprayed with non stick spray) over medium heat until hot. Place the sandwiches in the pan, cover, and cook until the bottom starts to turn golden brown, about 2 minutes. Uncover, turn the sandwiches over with a spatula (be careful if you’ve used grated cheese so the filling stays put), press them down a bit with the spatula and cook uncovered until the bottom is golden brown and crisp, about 3 minutes. Flip one more time, and cook until the bottom crust is fully golden brown and crispy, another minute or two.
Transfer the sandwiches to the cutting board, let them sit for two minutes for the cheese to firm back up a bit, then cut in half and serve.