Add about 2 inches of oil to a large cast iron skillet. Heat to 350 degrees F. Place a wire rack on top of a rimmed baking sheet. Set aside.
Place egg roll wrappers with a corner pointing at you. Spread each egg roll wrapper with 2 tablespoons of mashed potatoes. Leave about an inch without potatoes at the corners. Top each with 1 tablespoon of stuffing. Add 2 tablespoons of diced turkey. Add 3 or 4 green beans.
Whisk together the egg white with a splash of water. Set aside.
Fold up the top and bottom corners of the egg roll wrapper. Take one of the sides and tightly roll. Brush remaining corner that hasn't been folded with egg wash and continue rolling until sealed.
Once oil is hot, add egg rolls to the skillet and fry for about 2 minutes per side, until golden brown and crispy. Drain on prepared wire rack and serve immediately.
For the cranberry dipping sauce: heat a small saucepan over medium heat. Add cranberry sauce, spicy brown mustard and brown sugar. Whisk together. Simmer for 3 minutes. This sauce can be served hot or cold.