In a small bowl, whisk together miso, water, and dark brown sugar until combined.
Heat both sesame oils in a large sauce pan on medium high. Once the oil is hot, add ginger and garlic. Stir constantly, until garlic is lightly browned, about 1 ½ minutes.
Add kale, stirring constantly, until slightly wilted. Add miso mixture to kale; stir for one minute more until evenly combined and charring lightly on the edges. Enjoy immediately!