Place the soy sauce, lemon juice, vinegar, toasted sesame oil, ginger, and garlic powder in a large bowl and whisk to blend. Add the slabs of tofu and let marinate for 5 minutes.

Heat a large skillet, preferably cast-iron, over medium-high heat and add the tofu (reserving the bowl of marinade). Cook on one side until browned, about 2 minutes. Then turn the tofu over with a spatula and cook until nicely browned on the other side, 2 minutes. Transfer the tofu to a cutting board and cut it into 3/4-inch cubes. Return the tofu to the bowl containing the marinade.

Bring 4 quarts of water to a boil in a large covered pot over high heat. Add 2 tablespoons salt, and stir in the noodles. Cook according to the package directions until al dente, about 7 minutes.

While the pasta is cooking, heat the plain sesame oil in a cast-iron skillet over medium-high heat. Add the shallots, ginger, and garlic, and cook, stirring constantly, until aromatic, about 1 minute. Then add the broccoli, bell pepper, carrot, and zucchini, and stir-fry until the vegetables begin to soften, about 4 minutes. Cover the skillet and cook until the vegetables are crisp-tender, another 2 to 4 minutes.

Meanwhile, drain the noodles and add them to the tofu.

Season the vegetable mixture with salt, and add it to the tofu and pasta. Toss to combine, sprinkle with the sesame seeds, and serve.