Rinse sweet potato wedges with salted water to soften slightly.
Heat sesame oil in a large skillet over medium heat. Add sweet potato wedges; cook until light brown, about 2 minutes per side. Reduce heat to low and cover; cook, stirring occasionally, until browned, about 10 minutes.
Mix soy sauce, mirin, and honey together in a small bowl. Pour into skillet and stir until wedges are evenly coated, about 1 minute.