Vegetable Egg-Drop Soup

Ingredients

• 1/2 ounce (about 5) dried shiitake mushrooms
• 8 ounces boned, skinned chicken breast
• 1 tablespoon cornstarch
• 1 tablespoon plus 2 tsp. soy sauce
• 3/4 teaspoon white pepper, divided
• 2 qts. vegetable broth or chicken broth
• 8 to 10 thin slices peeled fresh ginger
• 2 small carrots, roll-cut into 1-in. pieces
• 1 medium onion, diamond-cut into 1-in. pieces
• 1 stalk celery, V-shaped-cut into 1-in. pieces
• 1 slender zucchini, roll-cut into 1-in. pieces
• 1 large tomato, peeled*, diamond-cut into 1-in. pieces
• 4 long cilantro sprigs, small sprigs pinched off and stems cut into 1-in. pieces
• 1/2 teaspoon kosher salt
• 1 to 2 tsp. toasted sesame oil
• 2 large eggs