Combine the sugar, jalapeno, ginger, and aji mirin in a small saucepan and bring to a boil over medium-high heat, swirling to dissolve the sugar. Remove from the heat and allow to cool slightly, then strain (discard solids). Place the syrup in a mixing bowl and whisk in the soy sauce and sesame oil. While continuing to whisk, add the vegetable oil in a slow, steady stream until completely incorporated. Set aside.