Crack the eggs into a medium-sized bowl. Add the salt and pepper, then whisk until the yolks and whites are fully combined and slightly frothy. Set aside.

Place a non-stick skillet over medium-low heat. Add the butter (or oil) and let it melt completely, swirling the pan to coat the surface evenly.

Pour the whisked eggs into the pan. Allow them to sit undisturbed for a few seconds until the edges begin to set. Using a spatula, gently stir the eggs, pulling them from the edges toward the center. Continue this motion to create soft curds.

When the eggs are about halfway cooked and still slightly runny, sprinkle in the shredded cheese evenly. Gently fold the eggs to incorporate the cheese, allowing it to melt as the eggs finish cooking. Be careful not to overcook; the eggs should be soft and creamy.

Remove the scrambled eggs from the heat just before they're fully set, as they will continue to cook slightly from residual heat. Divide the eggs between two plates and serve warm.