In shallow dishes, mix the flour, salt and black pepper. Place the egg in another dish and the panko and thyme in a third. Dredge the eggplant in the flour, then egg, and then panko. Deep fry at 350 degrees until golden, about 5 minutes. Season lightly with salt and drain on paper towels.
MISO UDON NOODLES:
In a saucepan, heat the chicken stock and whisk in the miso and ginger. Season and check. Heat through and add scallions, tofu and noodles. In a bowl, whisk together vinegar, sesame oil, sugar and white pepper. Toss with greens and mushrooms to coat. Check for seasoning.
PLATING In large pasta bowls, ladle in the noodle soup. Slice the eggplant in half on the bias and place on top of the noodles. Top with salad.