Slice the cheese into 1/2-inch (1 cm) rounds.
Dredge with flour, dip into the egg mixture, and dredge with flour again. You can do this in advance and chill the cheese unitl needed.
Heat 1/4 inch (5 mm) of oil in a skillet over high heat until very hot.
Carefully fry the cheese, a few at a time, until golden brown on both sides.
Drain on paper towels.
Combine the onion, vinegar, olive oil, salt, pepper, arugula and mint in a small bowl and toss to combine.
Place a small bed of the mint and arugula mixture on each plate and top with the fried cheese.