Chilled Udon with Sweet and Spicy Chicken and Spinach

Name: Chilled Udon with Sweet-and-Spicy Chicken and Spinach
Ingredients: 2 to 3 tablespoons finely grated fresh ginger; 1 1/2 lb boneless skinless chicken breast halves; 1/3 cup soy sauce; 1/4 cup mirin (Japanese sweet rice wine); 1 teaspoon Asian chile paste with garlic; 2 teaspoons Asian sesame oil; 12 oz dried or 16 oz fresh udon noodles; 6 cups baby spinach, coarse stems discarded; Garnish: julienne scallions and toasted sesame seeds