Combine turkey, mashed potatoes, green bean casserole, salt, and pepper in a bowl. Stir until evenly combined.
Place an egg roll wrapper on a clean surface with one corner facing you, so it looks like a diamond. Place 3 tablespoons of filling onto the wrapper. Fold up bottom half of the wrapper and tightly fold in sides. Gently roll and seal with a couple of drops of water. Repeat with remaining wrappers and filling.
Place gravy in a small saucepan and stir in cranberry sauce. Heat on low until ready to use.
Heat oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C).
Place 4 egg rolls in the hot oil and cook until golden brown, about 4 minutes. Remove egg rolls using tongs and place on a paper towel-lined plate. Repeat with remaining egg rolls. Serve gravy on the side for dipping.