Place the potatoes and 2 tablespoons of salt in a large saucepan and cover completely with cold water. Bring to a boil, then reduce the heat to low and simmer for 20 to 25 minutes, until the potatoes are fork tender. Drain the potatoes.
Transfer the potatoes back to the saucepan and mash with a potato masher until smooth. Place over low heat and cook for 2 to 3 minutes, stirring constantly to dry out the potatoes. Gradually stir in the butter and cream until well incorporated. Transfer to a clean bowl and stir in the flour and cheese. Season with salt, to taste.
Heat 2 tablespoons of vegetable oil in a large skillet over medium-high heat. Using a 1/4-cup measure, drop the potato mixture into the skillet and cook for 2 to 3 minutes per side, until golden brown. Continue cooking the potatoes, adding more oil as needed.
To serve, top each potato cake with a dollop of sour cream and a few pomegranate seeds.