Place egg, remaining 1/2 cup milk, flour, pepper, and remaining 1 teaspoon salt in a large bowl and whisk until smooth, about 10 seconds. Add potatoes and stir until evenly incorporated. Heat a large nonstick frying pan or griddle over medium heat. Once the pan is ready, add enough butter to lightly coat the bottom when melted.

Place egg, remaining 1/2 cup milk, flour, pepper, and remaining 1 teaspoon salt in a large bowl and whisk until smooth, about 10 seconds. Add potatoes and stir until evenly incorporated. Heat a large nonstick frying pan or griddle over medium heat. Once the pan is ready, add enough butter to lightly coat the bottom when melted.