How to Make It
Combine broth, water, salt, ginger, and garlic in a large saucepan; bring to a boil over high. Reduce heat to medium, and simmer until fragrant, 10 to 15 minutes.
Meanwhile, bring a medium pot of water to a boil. Add eggs, reduce heat to medium, and cook at a vigorous simmer for 6 minutes. Drain; rinse eggs under cold water to cool. Peel eggs and cut in half lengthwise.
Remove broth from heat; remove and discard ginger and garlic. Stir in kale. Cover and set aside until kale is wilted, about 4 minutes. Transfer ½ cup broth to a medium bowl and whisk in miso and vinegar until smooth. Add miso mixture to broth in saucepan; whisk to combine.
To serve, ladle broth with greens into 4 serving bowls. Top each bowl with 2 egg halves, and sprinkle with togarashi.