Cut the potatoes into ½-inch-thick pieces. Soak them in a bowl of water for 20 minutes to remove the starch. Drain and dry the potatoes with a paper towel.
Combine the sugar, soy sauce, mirin, and 1 tbsp. filtered water in a small saucepan and bring to a boil over medium-high heat and cook, stirring frequently, until it comes to a boil. Lower the heat and cook for another minute. Remove from heat.
Heat the oil in a large nonstick or well-seasoned cast-iron skillet over low heat. Pan-fry the potatoes, turning frequently, until toasted (but not burned) on both sides and a toothpick pierces a piece easily, about 3 minutes per side. Transfer the potatoes from the pan to a bowl.
Clean out the skillet, add the sauce, and cook over low heat until it begins to boil, about 1 minute. Return the potatoes to the pan and cook, stirring with a spatula for another minute, or until they are coated with the caramelized sauce.
Remove from heat and serve topped with the sesame seeds.