Prepare soba noodles according to package instructions. Drain, toss with sesame oil to coat evenly, and divide into serving bowls. Set aside.
In a medium skillet over medium high heat, add oil and sauté mushrooms until lightly browned, about 4-5 minutes. Take off heat and add soy sauce to coat well. Divide mushrooms over cooked soba noodles.
Meanwhile in a medium pot, combine chicken stock, sesame oil and soy sauce; bring to a low simmer. Add baby spinach and stir until just wilted, less than a minute. Ladle hot stock and spinach over noodles and mushrooms. Top with remaining ingredients; halved soft-boiled eggs, sliced green onions and desired garnishes. Serve immediately.