Crack eggs into a bowl. Add a pinch of salt. Whisk vigorously until fully combined and slightly frothy — no streaks of white should remain.
Melt butter in an 8-inch non-stick skillet over medium heat until foamy but not browned.
Pour in eggs. Let them sit undisturbed 20 seconds until the very edges begin to set.
Using a spatula, gently push the cooked edges toward the centre while tilting the pan so the uncooked egg runs to the edges. Work around the whole pan.
When the eggs are just barely set on top but still slightly glossy, add shredded cheese to one half.
Fold the empty half over the cheese. Slide onto a plate immediately — the residual heat melts the cheese perfectly.
The interior should be soft and just-cooked, not rubbery. Serve right away.