In a medium mixing bowl, crack the 4 eggs and add the 1/4 cup of milk. Season with a pinch of salt and pepper. Whisk together until well combined and slightly frothy.
Heat the non-stick skillet over medium heat and add the tablespoon of butter or oil. Allow it to melt and coat the bottom of the skillet.
Pour the egg mixture into the skillet. Let it sit for a few moments until the edges start to set.
With a spatula, gently stir the eggs, pushing them from the edges toward the center. Continue to cook, stirring occasionally until they are mostly set but still slightly runny.
Once the eggs are almost done, sprinkle the 1/2 cup of shredded cheese over the top. Gently fold the cheese into the eggs, allowing it to melt and combine as the eggs finish cooking. Remove from heat when the eggs are creamy and the cheese is melted.
Serve immediately, garnishing with additional pepper or herbs if desired.