Begin by combining the softened butter and grated Parmigiano-Reggiano in a small mixing bowl. Stir them together until you achieve a smooth and well-blended mixture.

Next, assemble the sandwiches. Lay out four slices of sourdough bread and onto each, layer two slices of bacon and a slice of Cheddar cheese. Complete the sandwiches with the remaining bread slices.

Preheat a large skillet over medium heat. While waiting, apply a generous amount of the butter and Parmesan mixture to the top side of each sandwich. Once the skillet is hot, place the sandwiches in, buttered side down. Then, spread the rest of the butter mixture on the top sides of the sandwiches.

Allow the sandwiches to cook until they turn a golden brown, typically taking about 3 minutes per side. Monitor the heat to ensure they do not burn.

To serve, remove the sandwiches from the skillet and slice each diagonally in half. This method of cutting