Make clarified butter by heating butter in a saucepan over low heat until fat separates from milk solids (20-30 minutes). Skim impurities from the top with a spoon, then strain the liquid butter into a clean container until you reach the milky solids on the base (discard these). The butter should be free of impurities; if some remain, strain the butter through a piece of fine muslin. Clarified butter will keep for 3 weeks stored in an airtight container in the refrigerator.
Spread mustard over half the bread slices, then top with mortadella and pickles, then the provolone and season to taste. Sandwich with remaining bread, then trim off crusts and set aside.
Preheat oven to 200C. Heat 2 tbsp clarified butter in a large frying pan over high heat, add 2 sandwiches and fry, turning once, until golden (2-3 minutes each side). Transfer to a board and repeat with remaining butter and sandwiches. Carefully slice each sandwich into 4 finger sandwiches and transfer to an oven tray lined with baking paper.
To serve, bake finger sandwiches until cheese melts (4-6 minutes). Serve warm.