Put potatoes, onion, broth, butter, salt, pepper, and dry mustard in a 4-quart slow cooker. Gently toss seasonings through; level potatoes.
Cover; cook on LOW about 6 hours until largest cubes easily pierce. Keep lid closed; confirm tenderness before adding milk.
Whisk evaporated milk and cornstarch completely smooth. Gently stir into hot potatoes. Cover; cook on HIGH 25 to 30 minutes until edges bubble and liquid thickens.
Turn off cooker; fold in cheddar in 3 additions until melted, keeping cubes intact. Rest uncovered 10 minutes.
Serve hot. Gently reheat refrigerated leftovers to 165°F at center, adding 2 tablespoons milk per 2 cups potatoes as needed.