Pare potatoes and cut into chunks. Add potatoes to a large pot or dutch oven. Bring to a boil, reduce heat and cover. Cook for about 20 or 25 minutes until tender.
Remove from stove and stir in the cheddar cheese while the potatoes are hot. Add stick of butter and salt and pepper. Pour in the can of evaporated milk and whip on high speed until no lumps are seen and they are nice and smooth. Sprinkle with chives.
When I cook a pot roast, I will cook my potatoes in the roast until tender, remove and mash them..I omit the cheese when I do this. They are so good after cooking in the roast juice.