Clean and chop your potatoes into 1-inch chunks. If you like your mashed potatoes skinless, you can peel your potatoes beforehand but I find yellow flesh potatoes have a pretty thin skin, so I don’t bother to do that. Place the potatoes and the garlic cloves in a large stockpot and fill with water, so it covers the potatoes by 1-inch. Add 3 teaspoons of salt to the water and bring to a boil. Once boiling, lower heat to let the water simmer, and cook potatoes for 10 to 15 minutes, or until a fork pierces the potatoes easily.
While the potatoes cook, clean the leek by slicing it lengthwise and fanning them out under running water to remove the dirt and sand. Chop the white part and 1-inch of the green part of the leek. Add them to a pan with the butter and turn the heat to medium high. Cook the leeks until they soften and start to a look a little translucent, about 3 to 5 minutes. Remove from heat.
Once the potatoes are done, drain them in a colander, then place them back into the hot pan they cooked in.
Scoop into a large serving bowl, drizzle with the melted butter and garnish with chopped parsley.