In a medium saucepan, add the dashi, mirin, sugar, soy sauce, and salt.
Bring the broth to a gentle simmer. Once the broth is simmering, remove it from the heat. Cover with a lid and set aside.
To Cook the Quick Udon Broth (with Mentsuyu; optional)
Follow your mentsuyu bottle instructions to make the broth.
In a medium saucepan, combine the water, mentsuyu, and mirin. Bring it to a simmer over medium heat. Once simmering, remove the pot from the heat. Cover with a lid and set aside.
To Cook the Udon Noodles
Bring a large pot of water to a boil. When the water comes to a full rolling boil, add udon noodles and cook according to the package instructions. For fresh homemade udon, separate and untangle the strands of noodles with your hands, and cook for 10 minutes.
Using chopsticks, stir the noodles so they won't stick on the bottom of the pot.
Drain the noodles into a colander and run under cold water.
Once the noodles are cool enough to touch, rinse the starch off. Then change the faucet to hot water and run hot water to warm up the noodles.
Serve the hot udon noodles in individual bowls. Pour hot broth over the noodles and top with chopped green onions and optional shichimi togarashi.