Step 1
To a large bowl, add the radicchio, lettuce, shiso, tomatoes, dill fronds, carrots, cucumber, and chile and toss to combine.
Step 2
In a small sieve set over a bowl, place the ginger and press until you have 1 teaspoon of juice; discard the solids and reserve any remaining juice for another use. Add the olive oil, lemon juice, vinegar, soy sauce, miso, sesame oil, sugar, and salt and black pepper to taste and whisk until sheeny and thickened slightly, about 1 minute. Pour into 4 small ramekins and sprinkle with sesame seeds; set aside.
Step 3
In a large pot of salted water, boil the soba noodles until al dente, about 3 minutes for fresh noodles and 4–6 minutes for dried. Pour into a colander to drain, then rinse under cold running water until the water runs clear.
Step 4
To serve, use tongs to divide the noodles among 4 serving plates. Top each portion of noodles with one quarter of the lettuce mixture, then sprinkle with sesame seeds. Serve with the dressing on the side.