Cook eggs: Fill a medium saucepan with water. Bring to a boil, carefully place eggs inside (the water should cover the eggs by a 1⁄2-inch), and cook, about 6 minutes. Using a slotted spoon, remove eggs from pot and place in a bowl of cold water. Once cool, remove shells and halve eggs. Reserve water and saucepan for step 3.
Prep veggies & chili oil: Trim stem ends from mushrooms, then thinly slice caps. Peel and finely chop half of the ginger (save rest for own use). Peel and finely chop 2 large garlic cloves. In a small bowl, stir together 1 packet of chili garlic sauce packet (reserve 2nd packet for step 5) and 1 teaspoon oil.
Cook noodles: Return reserved saucepan of water to a boil. Add noodles, and cook until just tender, 3–5 minutes, stirring occasionally. Drain, then rinse with warm water.
Sauté aromatics: Heat 1 tablespoon oil in a medium pot over medium-high. Add beef and cook until brown. Add mushrooms and Bok choy cook, stirring occasionally, until mushrooms are browned and dry, 6-7 minutes. Add garlic and ginger and cook 1 minute more.
Simmer broth: Add 4 cups water and 1 teaspoon salt to the saute aromatics and bring to a boil. Cover and simmer 5 minutes to allow flavors to meld. Remove from heat, then whisk in remaining chili garlic sauce and all the miso.
Finish & serve: Add spinach to soup and stir until wilted. Season to taste with salt. Divide noodles between bowls, then ladle soup and vegetables over top. Garnish with egg halves, and top with as much furikake and chili oil as desired.