Peel the sweet potatoes and cut them into planks about ¼ inch thick, then cut the planks into sticks 2 to 3 inches long and square in cross section. Keep them as even as you can.

Soak the sticks in cold water with the salt for 15 minutes. The water will turn cloudy as the surface starch comes off.

Drain, rinse once, then spread the sticks on a clean towel and pat them completely dry. Wet sticks steam instead of frying.

Heat the oil to 320F in a deep pot. Fry the sticks in two batches for 6 to 8 minutes each, until pale gold and barely bubbling. Lift onto a rack and rest 5 minutes.

Raise the oil to 350F and fry each batch again for 1 to 2 minutes, until light amber and rigid. Drain on the rack.

In a wide skillet, combine the sugar, water, mirin, rice vinegar, and soy sauce. Bring to a boil over medium heat without stirring and cook 3 to 4 minutes, until the bubbles are small and slow and the surface looks thick, about 240F.

Cook another 30 to 45 seconds past that point. This is what makes the coating crystallize instead of staying sticky.

Take the pan off the heat, add all the fried sticks at once, and toss constantly. The syrup will look glossy, then turn cloudy, then go white and sandy as the sticks separate.

Spread the sticks in a single layer on parchment, scatter the black sesame seeds over them while the coating is still warm, and cool 20 minutes before eating.