In a bowl, pour the hot water into the dried shiitake mushrooms, set aside and let them soak for 15 minutes;
Cook the udon noodles according to package instructions;
Immediately drain and rinse under cold water to cool down the noodles to stop the cooking, and prevent them from sticking;
In a saucepan, add the stock, the water from the soaked shiitake mushrooms, you can add the mushrooms to the pan too or save for another recipe, and the rest of the broth ingredients;
Stir and cook till the sugar dissolves, set aside to cool down;
Assemble the bowl with the chilled noodles, carrots, edamame, pickled ginger, and the tofu "egg" if making, place a few ice cubes on top;
Pour in the cooled-down broth, top off the bowl with shredded nori, scallions, and sesame seeds;
Serve immediately before the ice melts! Enjoy!