Place potato cubes, onion, broth, butter, salt, pepper and dry mustard in a 4-quart slow cooker. Toss gently to distribute the seasonings and level the potatoes.
Cover and cook on LOW for about 6 hours until a fork enters the largest cubes easily. Keep the lid closed during cooking and confirm the potatoes are tender before adding the milk.
Whisk evaporated milk with cornstarch until completely smooth. Stir gently into the hot potatoes, cover and cook on HIGH for 25 to 30 minutes until the liquid bubbles around the edges and thickens.
Turn the cooker off and fold in cheddar in 3 additions until melted, keeping the potato cubes intact. Let stand uncovered for 10 minutes to settle the sauce.
Spoon into a serving bowl while hot. Reheat refrigerated leftovers gently with 2 tablespoons milk per 2 cups of potatoes as needed until the center reaches 165°F.