Udon Noodles with Fried Eggplant

Udon Noodles with Fried Eggplant, Walnut Miso3 green onions, white and green parts1⅓-inch (about 1 oz/25 g), peeled fresh ginger, cut into very fine matchsticks2 small eggplants (about 1 lb/500 g) about 1 cup/250 ml sunflower oil, plus1 tablespoon6 shallots, thinly sliced (about 1 cup/100 g)2 cloves garlic, crushed1¼ cups/120 g walnuts, lightly toasted and coarsely chopped3 tbsp/50 g sweet white miso paste⅔ cup/150 ml vegetarian dashi or vegetable stock from cube3 tbsp mirin2 tbsp soy sauce1 tbsp superfine sugar1 tbsp sake (optional)9 oz/250 g dried udon noodles½ cucumber, unpeeled, cored and cut into very fine strips (5 oz/150 g)saltCut each green onion into 2-inch/5-cm lengths. Slice each length in two, from top to bottom, and then cut each half into long strips, as thinly as you can. Place the onions and two-fifths of the ginger in a bowl of iced water and put in the fridge.Use a vegetable peeler to peel off 4 or 5 strips of stem the eggplants, from top to bottom, so you are left