In a skillet over medium heat, add the vegetable oil. Once hot, add the ground beef, breaking it up with a spatula. Season with 1 teaspoon of salt and black pepper. Cook until browned and fully cooked, about 7-10 minutes. Drain any excess fat and set aside.
In the same skillet, add a little more oil if necessary, and add the shredded hash brown potatoes. Cook until they are golden brown and crispy, about 5-7 minutes, stirring occasionally. Once done, remove them from the skillet and set aside.
In a mixing bowl, crack the eggs and add the remaining teaspoon of salt and water. If using, add the pancake batter. Whisk until well combined and slightly frothy.
Spray the skillet with nonstick spray and return it to medium heat. Pour the egg mixture into the skillet, tilting it to ensure even coverage. Cook without stirring for about 3-4 minutes until the edges begin to set.
Once the omelette is mostly cooked, add the cooked ground beef, hash browns, and shredded Cheddar cheese on one half of the omelette. Carefully fold the other half over the fillings and press down gently.
Let the omelette cook for another 2-3 minutes, allowing the cheese to melt. The omelette should be fully set but still soft.
Slide the omelette onto a plate and top with chopped tomatoes, dill pickles, ketchup, and mustard. Serve immediately for the best experience!