Place apples, lemon juice, cider, sugar and cinnamon in a medium pot over medium high heat and cook down into a thick sauce, stirring occasionally, 15 minutes. Remove from heat and stir in cranberry sauce to warm through and combine.
Place potatoes and water or milk in a bowl and cover with plastic. Microwave 2 minutes on high to slightly reheat and loosen potatoes. Stir them up with the liquid to make them workable again. Combine cheese, scallions and nutmeg with potatoes and adjust salt and pepper.
Add a drizzle of vegetable oil and a pat of butter to your preheated skillet then score the potatoes and cheese mixture in half. Using the first half of the potatoes, make 6 (3-inch across and 1/2-inch thick) potato cakes and space them evenly around the pan. Cook the cakes until golden all over, 3 minutes per side, then remove and garnish with paprika, if using, and repeat with remaining ingredients.
Serve potato-cheddar cakes with warm cran-apple sauce for topping.
* To make fresh smashed potatoes, cook off 2 1/2 pounds of small new skin potatoes until tender and smash them up with some milk or stock and butter, salt and pepper to taste.