In a medium bowl, mix together the chopped salmon, sesame oil, soy sauce, and mint leaves.
Place a sheet of nori, shiny side down, on a work surface.
Place 1/4 cup of the rice on the left side of the nori sheet. Using wet fingers, form the rice into a 3-inch square, leaving a 1/2-inch border.
Place about 2 tablespoons of the salmon mixture, diagonally, in a 1/2-inch wide strip, on the rice, with the top of the salmon mixture facing the top left corner.
Place a spear of asparagus on top of the salmon. Starting with the bottom left corner, roll the nori over the filling. Continue to roll, ice cream cone-fashion, working towards the right corner of the nori. Seal the edge of the hand roll with water or a few grains of the cooked rice. Repeat with the remaining ingredients.
Arrange on a serving platter and serve with wasabi, sweet pickled ginger and soy sauce.