In a large pot, bring 4 quarts of water to a boil and then add the two tablespoons of Kosher salt.
While the water heats, make the dressing. Chop the peeled ginger, then combine the miso paste, chopped ginger, soy sauce, and lime juice in a blender jar. Blend at medium speed until smooth. Add the egg, blend again until combined. Running the blender at the slowest possible speed, drizzle in the oil slowly, until the dressing becomes smooth. Add the pepper to taste. Salting the dressing is unnecessary because of the miso and soy sauce.***
Once the water in the pot begins boiling, add the noodles and cook them, stirring often to prevent clumping. Once they are al dente, drain the noodles and rinse them well under cold water. Drain the noodles as well as you can, then spread them out on a baking sheet to cool.
Prepare the vegetables in your salad by peeling and coarsely grating the carrots. Next, thinly slice the scallions on the bias. Finally, carefully use a mandoline or sharp knife to thinly slice the radishes. Put them in a large serving bowl.
Combine the cooled noodles with the carrots, scallions, and radishes. Drizzle the miso dressing over the salad and toss to distribute. Serve cold or at room temperature.
This soba salad is best consumed immediately or within 2 hours of dressing the noodles and vegetables.