Whisk the eggs, milk, and 2 teaspoons salt together in a medium bowl.
Put the butter in a cold large (12-inch) saute' pan and place it over low heat. Allow the butter to melt almost completely, then add the egg mixture.
Cook over medium-low for 8-10 minutes, stirring occasionally with a rubber spatula. When the eggs start to make small clumps, stir them more rapidly, scraping the bottom of the pan, and cook another 4-5 minutes.
When the eggs are almost cooked, turn off the heat and continue to stir the eggs rapidly until they're soft and custardy (when you pull the spatula through the eggs, they will be soft but they will stay in place).
Stir in the Pecorino and 2 teaspoons pepper.
Spoon the eggs over the toasted bread and serve hot with extra Pecorino.