Kombu Chicken Soup with Carrots and Mushrooms

Name: Kombu Chicken Soup with Carrots and Mushrooms
Ingredients: 10 ounces mature spinach (about 1 bunch), trimmed; 3 6x4-inch pieces dried kombu; 6 cups homemade or store-bought low-sodium chicken stock; 1 cup bonito flakes; 2 tablespoons mirin; 2 tablespoons soy sauce; Kosher salt; 2 boneless, skinless chicken breasts, halved lengthwise, thinly sliced crosswise; 1 medium carrot, peeled, cut into 2-inch matchsticks; 4 ounces shiitake mushrooms, stemmed, thinly sliced; Toasted sesame seeds (for serving)