Heat the olive oil in a large pot over medium heat. Add the onion and cook for 3 minutes until it starts to soften.
Stir in the garlic and ginger. Cook for 1 minute until fragrant.
Add the potatoes and lentils to the pot. Pour in the vegetable broth and bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 25 minutes until the lentils and potatoes are tender.
Ladle about 1 cup of the hot broth into a small bowl. Whisk in the miso paste until smooth, then stir the mixture back into the pot.
Add the kale and cook for 3 more minutes until it wilts. Season with salt and black pepper to taste before serving.