Using a biscuit cutter, cut the watermelon slices into medallions. Use a knife to trim uneven edges so it sits flat on the plate.
In a medium mixing bowl, toss arugula with chopped mint, olive oil, lemon juice, salt, and pepper.
Arrange the watermelon medallions on a plate, and top each with a handful of arugula mixture.
Sprinkle each with crumbled goat cheese and chopped walnuts.
Finish with a dash of aged balsamic vinegar.