Place the potato chunks in a large pot and fill with water to cover.
Bring the potatoes to a boil on medium-high heat and continue to boil until the potatoes are fork tender, 20-25 minutes.
Place 6 tablespoons of butter, cream and garlic in a small saucepan and bring up to a simmer on medium-low heat. Cover to keep hot.
In a large saute pan melt the remaining 2 tablespoons of butter on medium heat and saute the leeks for about 1 minute.
Add the kale to the leeks and continue to saute for an additional 2 minutes. Season with salt and pepper.
Pour the broth over the kale and leek mixture, stir and cover.
Allow the mixture to cook until the kale has wilted and the liquid has cooked off, about 7 minutes.
Once the potatoes are fork tender, drain them and place them back into the pot.
Begin mashing the potatoes, while adding the cream mixture a little at a time, until the potatoes are smooth and creamy. Season with salt and pepper.
Fold the leeks and wilted kale into the potatoes, adjust the seasoning and serve.