To make the dressing: Put the soy sauce, vinegar, ginger, brown sugar, sesame oil, red pepper flakes, garlic and 2/3 cup of the olive oil into a blender. Blend until completely emulsified. Taste the dressing and adjust to your taste, adding more vinegar or sugar as needed. Pour half of the dressing into a jar and refrigerate for the salad.
Put the tofu cubes into a bowl and pour over the remaining dressing. Cover and refrigerate for at least an hour.
Remove the tofu from the dressing and pat dry. Heat the remaining 2 tablespoons olive oil in a nonstick skillet over medium-high heat. Cook the tofu on all sides until nicely browned and crisp, about 10 minutes. Toss in the sesame seeds and cook for another minute. Remove to a paper towel-lined plate.
To assemble the salad, put the mixed greens, halved tomatoes and sliced onion in a large bowl. Pour on half the remaining dressing, reserving the rest for later use. Toss to coat. Arrange the tofu and mandarin oranges all over the greens. Serve immediately.