Prepare the Homemade Broth: In a medium-sized saucepan, combine dashi stock with mirin, sugar, soy sauce, and kosher salt. Heat over medium flame until just before boiling—allowing the flavors to meld gently. Remove from heat once small bubbles form around the edges, cover with a lid, and let it rest to develop a rich, delicate taste.
Make the Quick Broth Alternative: If using mentsuyu, measure according to your brand’s dilution instructions. Typically, blend mentsuyu, water, and mirin in a saucepan. Warm this mixture until it simmers gently, then take off heat and cover. This shortcut broth offers convenience without sacrificing flavor.
Cook the Udon Noodles: Bring a large pot of water to a rolling boil. Add the udon noodles and cook following the package directions — frozen noodles typically need about 1 minute, while dry noodles require a bit longer. Stir occasionally with chopsticks or a fork to prevent sticking and promote even cooking.
Drain and Prepare for Serving: Once noodles are tender and chewy, drain them well using a colander or a fine-mesh strainer. Place the hot noodles evenly into serving bowls.
Assemble and Garnish: Pour the steaming broth over the noodles, ensuring each bowl is evenly filled. Sprinkle thinly sliced green onions on top and add shichimi togarashi for a subtle spice, if desired. Customize with additional toppings like crispy tempura, tofu cubes, or grilled fish cake to turn the soup into a heartier meal.