Udon Noodles with Shiitake Mushrooms in Ginger Broth

Name: Udon Noodles with Shiitake Mushrooms in Ginger Broth
Ingredients: 8 ounces Japanese udon or soba noodles; 2 teaspoons sesame oil; 2 teaspoons vegetable oil; 1 ½ tablespoons minced fresh ginger (1 ½-inch piece); 2 shallots, very thinly sliced; ¼ pound (about 12) shiitake mushrooms, stemmed, caps wiped clean and quartered; 2 cups homemade or low-sodium canned chicken stock; 1 teaspoon rice-wine vinegar; 2 teaspoons low-sodium soy sauce; 3 cups (about 3 ounces) spinach, tough stems discarded, rinsed well, drained, and cut into 2-inch-wide strips; 4 scallions, thinly sliced diagonally into 2-inch pieces