Using a sharp knife, make 3-4 small cuts (about 1/2 inch deep) around the perimeter of each bologna slice. This prevents the bologna from curling up into a cup shape while frying.

Heat a large skillet over medium heat. Add the butter (or oil) and let it melt and coat the bottom of the pan. Place the bologna slices in a single layer in the hot skillet. Fry for 2-3 minutes per side, or until deeply browned and crispy to your liking. The edges will crinkle and crisp up beautifully. Remove the bologna from the skillet and set aside on a plate.

If desired, use the same skillet to toast the bread, soaking up any remaining bologna flavor. Place the bread slices in the skillet and toast for 1-2 minutes per side until golden. If adding cheese, place one slice of cheese on two of the toasted bread slices during the last minute of toasting, covering the skillet with a lid for about 30 seconds to help the cheese melt quickly.

Spread mayonnaise on one side of each bread slice and mustard on the other (or your preferred condiment combination). Place two slices of fried bologna on one of the bread slices, then top with a cheese-melted bread slice (if applicable) or the second plain toasted bread slice.

Slice the sandwiches in half diagonally and serve immediately with chips, pickles, or a side salad.