Sushi rice is a short-grain starchy rice that works just like Italian Arborio to thicken this Asian-flavored dish.
Combine miso and 6 cups water in large glass measuring cup, and whisk to blend. Heat 5 minutes in microwave, or until boiling. Stir well.
Heat 1 Tbs. oil in deep skillet or Dutch oven over medium-high heat. Add eggplant, and cook 6 to 8 minutes, or until browned and tender, stirring occasionally. Transfer to bowl.
Heat remaining oil in same skillet over medium-high heat. Add ginger and garlic, and sauté 30 seconds, or until fragrant. Add rice, and cook 2 minutes, stirring constantly. Add sake, and cook 1 to 2 minutes, or until liquid is almost completely absorbed. Add 1/2 cup miso broth; cook and stir until broth is almost absorbed. Continue adding broth, 1/2 cup at a time, and cook 8 minutes, stirring often and allowing rice to absorb most of liquid before adding more.
Stir in bok choy in batches, and cook 3 to 4 minutes, or until leaves are wilted. Add green onions and mushrooms, and cook 10 minutes more, adding liquid 1/2 cup at a time. Stir in eggplant and cook 2 minutes more, or until rice is tender and eggplant is hot. Remove from heat, stir in sesame oil, and season with salt and pepper.