In a large skillet over medium heat, add the breakfast sausage. Cook until browned, about 5-7 minutes. Transfer to a bowl and set aside.
In a mixing bowl, whisk together the eggs, half and half, salt, and pepper. Melt the butter in the skillet, pour in the egg mixture, and scramble until fully cooked, about 3-4 minutes. Remove from heat.
Once the eggs have cooled, add sausage, hash browns, and cheese to the egg mixture. Stir until combined.
Lay an egg roll wrapper on a flat surface, place a spoonful of filling in the center, fold the bottom corner over, fold in the sides, and roll tightly. Seal with water.
Heat vegetable oil in a frying pan. Fry egg rolls until golden brown, about 3-4 minutes on each side. Use a slotted spoon to remove and drain on paper towels.
Serve warm with your favorite dipping sauces.