Cut the sweet potatoes rangiri style: slice a wedge off the end on a steep diagonal, roll the potato a quarter turn, and cut again at the same angle. Continue down the potato for irregular wedges about 1 ½ inches long.

Soak the wedges in cold water 10 minutes to remove surface starch. Drain and dry completely on a towel.

Heat ¾ inch of oil in a wide heavy pan to 325F. Fry in two batches, 7 to 9 minutes per batch, turning halfway, until a skewer slides in easily and the cut faces are pale gold.

Raise the oil to 375F and return all the wedges for 60 to 90 seconds to set a crisp shell. Lift to a wire rack, not paper towels.

Pour off the oil and wipe the pan. Add the sugar, honey, mirin, soy sauce, water and salt over medium heat. Stir only until the sugar dissolves, then stop stirring.

Let the syrup bubble 2 to 3 minutes until it darkens slightly and the bubbles get larger and slower. Test a drop on a cold plate: it should turn tacky within 10 seconds.

Turn off the heat, add the fried wedges, and fold them through the syrup about 30 seconds until every face is coated and shining. Sprinkle the black sesame seeds over while the glaze is still wet.

Turn them out onto lightly oiled parchment and separate the pieces so none touch. Cool 10 minutes, until the glaze sets glossy and slightly tacky.