Heat skillet to medium (we really like cast iron for this if it’s available, but if not use a non-stick pan)
Assemble the sandwich: One and a half slices of Muenster (rip the half slice into pieces and spread around the slice), spread jam over cheese, and add a handful of arugula. Top with the second slice of bread.
Spread a thin layer of mayo on this slice. If you’re making multiple grilled cheeses, first assemble them all before you start griddling.
Place the sandwich mayo side down in the skillet. Spread mayo on the bread slice now facing up and cook 3 minutes, or until bread is toasty brown. Turn and repeat. Your stove top and pan may require slightly different cooking times.