In a large saucepan, melt 2 tablespoons butter over medium heat. Add leeks, and cook, stirring occasionally, until softened, about 4 minutes. Add parsnips, and cook, stirring occasionally, until they begin to soften, about 5 minutes more. Add potatoes and 3 cups cold water; bring to a boil. Cover and reduce heat to a gentle simmer. Cook until parsnips and potatoes are very tender and begin to fall apart, about 20 minutes.
Drain in a colander. Press hot parsnips and potatoes through a ricer back into saucepan over low heat. (Alternatively, mash by hand.) Add remaining 2 tablespoons butter and the milk, and combine well. Season with salt and pepper, and serve immediately.