Whisk Miso, Mirin, Sake and brown sugar together until smooth in a small bowl. Cut eggplant lengthwise and score with crosshatches, spread olive oil on a plate and coat cut sides. If using a grill with broiler, heat grill on medium high, and cook for 3-4 minutes on cut side. Rotate and turn on broiler, cook for 3-4 minutes, then flip to skin side down, spread Miso mixture evenly on cut side and cook for 3-4 minutes until bubbling and browning. When using an oven, cook in a large pan with a little extra oil skin side down for 3-4 minutes, turn over and cook for 3-4 minutes, then place on a cookie sheet covered in foil, spread Miso mixture evenly on cut side and broil for 3-4 minutes until bubbling and browning.