The Project: Iced Somen Noodles With Chicken And Vegetables With Spicy Ginger Sesame Sauce

Name: The Project: Iced Somen Noodles With Chicken And Vegetables With Spicy Ginger Sesame Sauce
Ingredients: 2 eggs; 2 teaspoons vegetable or canola oil, divided; 3 bunches (300 grams) dried somen noodles; 3 cups ice cubes; Steamed chicken; 2 cucumbers (Japanese or Persian), peeled and cut into matchsticks 1/8 -inch wide and about 3 inches long; 1 large carrot, peeled and cut into matchsticks 1/8 -inch wide and about 3 inches long; 1 large green pepper, cut into matchsticks 1/8 -inch wide and about 3 inches long; 1 bunch chives, chopped (about 1/4 cup) or 3 green onions, thinly sliced crosswise (white and green parts); 1 small bunch daikon (radish) sprouts, trimmed to remove roots, optional as garnish; 6 to 8 shiso leaves, thinly sliced, optional as garnish; 1 teaspoon toasted sesame seeds; Spicy ginger sesame sauce; 2 small (or 1 large) chicken breasts, about 1 pound total; 2 tablespoons sake; 1 green onion, white part cut crosswise into 1/8 -inch slices (green and root tip discarded); 1 tablespoon peeled and thinly sliced ginger (from a 1-inch piece); 1 teaspoon sesame oil