Swoon. This is the grown-up grilled cheese of your dreams. Apples, Dijon mustard, and arugula take it well outside the kid zone.
Spread mustard on 1 side each of bread slices. Divide thinly sliced apple among 2 of the bread slices; top each with 1 Havarti cheese slice. Top with remaining bread slices, mustard sides down.
Cook sandwiches in unsalted butter on a hot griddle over medium-high until golden brown, 3 to 5 minutes per side.
Gently pull sandwiches apart, and top apples on each with arugula. Put sandwiches back together, and serve.