Bring a large pot of water to a boil and cook the noodles according to package directions until al dente. Drain and rinse in cold water, and set aside.
Press the slabs of tofu between a clean dish towel or a few layers of paper towels to absorb some of the water. Heat a large cast iron or non-stick skillet over medium heat. Place the tofu in the hot skillet, and cook undisturbed, until it turns deep golden-brown, 3-5 minutes per side. Transfer the tofu to a cutting board and slice each piece into 1/2-inch spears. Set aside.
Heat oil in the skillet over medium heat. Sauté the garlic and ginger for 2 minutes, until golden and fragrant. Transfer to a large bowl. Add the peanut butter, hot water, rice vinegar, sesame oil, soy sauce, sugar and crushed red pepper flakes. Whisk together until smooth. If needed, add up to 2 more tablespoons of hot water to reach the consistency of heavy cream. Add the soba noodles, and toss to coat. Add the cucumber, scallions, and sesame seeds, and toss until incorporated. Serve topped with the sliced tofu.