Step 1

Let 1 tablespoon of the unsalted butter sit at room temperature until softened. Spread onto one side of 2 slices sourdough bread.

Step 2

Whisk 2 large eggs and 1/4 teaspoon kosher salt together in a medium bowl until combined.

Step 3

Melt the remaining 1 teaspoon butter in a medium nonstick skillet over medium-low heat. Pour in the egg mixture. Using a rubber spatula, scramble the eggs, stirring occasionally and pushing the cooked parts from the edges of the pan to the center, until they are just set but not dry. Transfer the eggs to a plate.

Step 4

Remove the pan from the heat and wipe the pan clean. Place 1 bread slice butter-side down into the pan. Top with 2 slices of the cheese, the eggs, and then the remaining 2 slices cheese. Close the sandwich with the remaining bread slice butter-side up. Press the sandwich slightly to close.