Preheat oven to 400ºF. Slice eggplant into matchsticks (see pictures above). Lightly toss in sesame oil then arrange eggplant on a sheet pan in a single layer. Bake for 10-12 minutes, until they start to soften. Combine miso, sugar and sake (or water) in a small bowl. Pour over eggplant and lightly toss. Bake for another 5 minutes.
Bring a pot of water to boil and cook udon noodles according to package. Drain and set noodles aside.
Heat oil in a skillet on medium heat. Add garlic and sauté for 1 minute. Add in ground meat and cook for another 3 minutes, breaking up the meat and stirring until no longer pink. Lower heat.
In a small bowl, whisk together soy sauce, oyster sauce and mirin. Add the sauce, eggplant and noodles to the skillet and stir until for about a minute until combined.
Serve with chopped green onion and a sprinkle of sesame seeds!