Heat the cast-iron skillet over medium heat until a light sizzle is heard when a drop of water is added, about 160°C (320°F).
Add the butter or oil to the skillet, letting it melt and coat the surface evenly. The fat should shimmer gently without smoking.
Place the bologna slices into the pan in a single layer, making sure they aren’t overlapping. Let them sizzle and curl at the edges, about 2-3 minutes, until they turn golden and crispy on the underside.
Flip each bologna slice carefully with the spatula, allowing the other side to crisp up for another 2-3 minutes. The slices should be golden brown and slightly crispy, filling the air with a smoky aroma.
While the bologna fries, toast the bread slices in a toaster or toaster oven until deep golden brown and crisp on the outside.
Transfer the fried bologna slices to a paper towel-lined plate to drain excess fat, which helps keep the sandwich from becoming greasy.
If using cheese, place a slice on top of the hot bologna slices in the skillet to melt slightly, about 30 seconds.
Spread mustard or mayo on one side of each toasted bread slice, adding tang or creaminess as desired.
Assemble the sandwich by layering the crispy bologna (with cheese if using) on one bread slice, then top with the second slice of bread.
Optionally, press the sandwich gently in the skillet for about a minute to meld the flavors and crisp the bread further, then remove and let rest for a minute.
Cut the sandwich in half to reveal the crispy edges and juicy bologna. Serve immediately with pickles or chips for added crunch and flavor.