Press extra-firm tofu for 15 minutes to remove moisture, then cut into 1-inch cubes and toss with a splash of soy sauce.
Heat sesame oil in a large pot over medium heat; add minced garlic and grated ginger, sautéing for 60 seconds until fragrant.
Pour in the vegetable broth and bring to a gentle simmer over medium-high heat.
In a small bowl, whisk miso paste and tahini with 1/4 cup of the warm broth until smooth, then stir the mixture into the pot along with the soy milk.
In a separate non-stick skillet, sear the tofu cubes over medium-high heat until golden brown on all sides, approximately 8 minutes.
Add the high-protein noodles and edamame to the simmering broth and cook according to the noodle package instructions, typically 4 to 6 minutes.
Divide the noodles, edamame, and broth equally into two large bowls.
Top each bowl with the seared tofu, one halved soft-boiled egg, and sliced green onions before serving immediately.