Cook the parsnips and potatoes separately in boiling salted water until they are tender. Drain and mash; mix together with salt and pepper.
Cook the sausage in a small amount of the bacon fat or butter in a large skillet over medium heat until browned, crisp, and cooked through. Set aside and keep warm.
Pour the fat from the sausages into a saucepan. Add the remaining bacon fat or butter and let it melt. Stir in the potatoes and parsnips and beat until creamy, over medium heat, adding hot milk to make a lighter consistency, if you prefer.
Spoon the mashed vegetables onto a serving plate and top with the sausages.