Prepare the tofu. Cut the tofu block in half. Place the halves in a large shallow dish on top of a clean tea towel (without terrycloth nubs.) Cover with another towel or paper towels. Place a second dish that would fit inside the first, on top and place something heavy inside. After 5 or 10 minutes the tea towels will have absorbed excess water.
While the tofu is pressing, trim any tough stalk away from the shallots. Chop them finely. Chop the spinach into 1-inch pieces.
Cut the pressed tofu into ½-inch cubes. Heat a large skillet or wok over medium high flame. Add the first tablespoon of oil and wait about 30 seconds. Add the tofu and stir-fry until it is golden and crispy on most sides, 5 to 10 minutes. Remove from the pan and set aside on paper towels.
Heat a large pot of water to boil for edamame and the noodles.
Heat the remaining tablespoon of oil in the skillet. Add the shallots and cook about a minute. Add the spinach, season with salt and stir until the spinach wilts. Place the tofu on top of the spinach, turn the heat to low and keep warm.
When the pot of water begins to boil, add the edamame and soba noodles, stirring so the noodles don’t stick together. Boil gently until the noodles are just tender, 4 to 6 minutes. Drain in a colander. Place in a large serving bowl. Top with the spinach and tofu. Sprinkle with soy sauce and garnish with the nori strips, if desired.