In a large enameled Dutch oven or stock pot, add tomato paste, soy sauce, miso, yuzu, garlic and vegetable broth. Simmer for 10 minutes.
Next, add tofu, scallions and mushrooms and simmer for 10 minutes longer. Taste and add salt if needed. Reduce heat and cover until ready to serve.
While the broth is simmering, cook udon or ramen noodles according to the package's instructions. When cooked through, drain and rinse under cold water to stop the cooking process. Add one teaspoon of sesame oil to the noodles, toss and set aside.
In a saucepan, bring 5 cups of water plus one tablespoon of white vinegar to a boil. Crack one egg into a small bowl and gently tip it into the boiling water. Cook for about three minutes or until the whites have set. Using a slotted spoon, remove the egg from the boiling water and place into a bowl of ice water. Repeat until all eggs are cooked.
To plate, scoop a serving of noodles into the bottom of each bowl, ladle over broth and top with poached egg. Garnish with scallions and hot chili oil if desired. Enjoy!