Step 1

Cook eggs in a medium saucepan of boiling water for 6 minutes. Immediately transfer to a bowl of ice water and let sit until cool, about 5 minutes. Carefully peel eggs under running water (yolks will be partially set); set aside.

Step 2

Heat oil in a medium saucepan over medium. Add kale and cook, tossing, until wilted, about 2 minutes. Add mirin, soy sauce, miso, and ¼ cup water and stir until miso is dissolved. Bring to a simmer over low heat, partially cover, and cook until kale is tender, 5–10 minutes.

Step 3

Divide oats and yogurt among bowls, spooning yogurt into centers. Spoon kale mixture along with juices over yogurt, then place an egg on top. Season eggs with salt, then top with scallions and furikake. Drizzle with chili oil.

Step 4

Do Ahead: Eggs can be boiled 3 days ahead (do not peel); cover and chill. Braised kale can be made 4 days ahead; cover and chill.