Bring a large pot of water to a boil and salt it.
Add the udon noodles and cook, stirring occasionally, until tender but not mushy, about 5 to 7 minutes.
Drain and rinse thoroughly under cold running water to cool them completely.
Set aside.
While the noodles cook, combine the cooked soybeans, nuts, 2 tablespoons (30 ml / 1 fl oz) of sesame seeds, soy sauce, and a few grinds of black pepper in a blender.
Add 3 cups (720 ml) of ice water and blend on high until completely smooth and creamy. If the broth seems too thick, add a little more water until it reaches your desired consistency.
Taste and adjust seasoning with more salt if needed.
Drain the cooled noodles well and divide them between two serving bowls, mounding them in the center. Ladle the chilled bean broth around the noodles.
Garnish with sliced cucumber, a sprinkle of sesame seeds, a drizzle of dark sesame oil, and optional fresh chiles and scallions.
Serve immediately.
While udon is delicious, traditional Kongguksu is often made with thin wheat noodles called somen. Soba noodles or even spaghetti would also work in a pinch.
