Place chopped potatoes into a saucepan and covered with water. Boil until the potatoes are softened. Drain the water off and set potatoes aside.
Place the chopped onion in the same saucepan you cooked the potatoes in. Add the oil. Saute until the onions are brown and softened. You can skip this step but I think it mellows the flavor of the onions and adds more flavor.
Add the cooked potatoes back into the pan with the browned onions.
Add the milk and salt and pepper.
Heat and stir until warmed through. To make the soup thicker smash a few of the potatoes on the side of the pot and stir them in.
Place the soup into bowls and sprinkle with cheese and chives if desired.
Serve warm and enjoy!