Add cubed potatoes to a bowl filled with cold water and soak for at least 10 minutes.
Preheat oven to 400°F or air fryer to 375°F. If using the oven, grease or line a baking sheet for roasting.
Drain soaked potatoes and pat each cube dry with a towel. Toss with oil and place on baking sheet/air fryer basket. Roast for 30-35 minutes in the oven, or about 20 minutes in the air fryer.
When the potatoes are about 5 minutes from being done, add the remaining ingredients to a saucepan and bring to a simmer over medium low heat. When the sugar is dissolved and the sauce has reduced, turn off the heat and add potatoes. Mix until the potatoes are evenly coated.
Add potatoes back to baking sheet/air fryer basket and roast an additional 2-4 minutes until browned and crisp. The sauce burns easily so keep a close eye on them.
Garnish with toasted sesame seeds and chopped green onions if desired.