Heat the olive oil in a medium saucepan over medium heat. When the oil is shimmering, add the shallots, salt and pepper and cook stirring occasionally for 12-15 minutes until the shallots have browned and caramelized. (If the shallots are drying out or starting to burn, add a little water and reduce the heat.)

To assemble the sandwiches, spread one side of the bread with whole grain mustard. Arrange the cheddar, apples, arugula and shallots on two of the bread slices and top with the remaining bread. Lightly butter the outside of the sandwiches.

Melt 1 tablespoon butter in a skillet or griddle over low to medium heat and add the sandwiches. Cook until the bread has browned and the cheese has started to melt. Flip continue cooking until the bread is golden brown and the cheese has fully melted. (Cooking low and slow is best--be patient!) Serve immediately.