For the vinaigrette: place dashi, soy sauce, lemon juice, rice wine vinegar, oil, garlic and onion in a blender. Season with black pepper. Whirl until smooth. Taste and adjust seasonings.
For the tomato salad: Cut tomatoes so they’re in different shapes but roughly all the same size. Add the scallions, followed by the red onion. Season to taste with salt and pepper. Taste the vinaigrette and adjust with more vinegar and soy if necessary.
Dress the salad by pouring about half of the vinaigrette and gently toss. Serve immediately or store vinaigrette up to three days in advance. Garnish with thinly sliced shiso leaves.