Prepare grill or broiler.
Place the leeks, eggplants, fennel, and garlic in a grill basket on a grill rack or on a broiler pan; cook 10 minutes or until tender, turning frequently. Remove the leeks, eggplant, and fennel from the heat, and cook the garlic for an additional 5 minutes.
Combine mirin and water in a small saucepan over medium heat; bring to a boil. Reduce heat; simmer 3 minutes.
Squeeze garlic cloves to extract pulp; place pulp in a blender. Add the mirin mixture and miso; process until smooth. Pour the sauce over the vegetables, and toss well to coat.