Bring a pot of water to a boil and cook the udon noodles according to package directions; drain and set aside.
Place the egg in a small saucepan of boiling water for 6.5 minutes, then transfer immediately to an ice bath, peel, and slice in half.
Press the firm tofu to remove excess moisture, then cut into 1/2-inch cubes.
Heat the sesame oil in a large skillet over medium-high heat.
Add the sliced leeks and bell peppers to the skillet, sautéing for 3-4 minutes until the leeks are softened and fragrant.
Stir in the minced garlic, grated ginger, and tofu cubes, cooking for another 5 minutes until the tofu is lightly golden on the edges.
Add the cooked udon noodles, shelled edamame, tamari, and nutritional yeast to the skillet.
Toss everything together for 2 minutes until the noodles are well-coated and the edamame is heated through.
Season the mixture with sea salt and black pepper.
Remove from heat and gently fold in the rucola until it just begins to wilt from the residual heat.
Divide the noodle mixture into a bowl and top with the soft-boiled egg halves.