Heat a large pot of salted water over high heat. While waiting for water to boil, and cut into 1-2 inch cubes
When water boils, add potatoes and cook for 15-20 minutes until very tender. Drain and return to pot.
While potatoes are boiling, melt butter in a medium saucepan over medium heat. Add white/light-green parts of green onions and cook, stirring occasionally, until onion is softened and fragrant, about 1-2 minutes.
Add kale, reduce heat to medium-low, and continue to cook until kale is completely wilted and starting to lightly brown, about 4-5 minutes. Remove from heat.
Mash potatoes to desired consistency with a potato masher or ricer.
Add butter-onion-kale mixture to potatoes along with 1/4 cup of milk, ½ tsp salt, and ¼ tsp pepper.
Mix until smooth. Add more milk as needed to obtain desired consistency, and adjust seasoning with salt and pepper to taste.
Serve immediately or keep warm over low heat, stirring occasionally, until ready to serve. Top with green part of green onions for garnish.