In a medium bowl, crack open your large eggs and sprinkle in the kosher salt and white pepper. Using a whisk or fork, beat the mixture vigorously until the eggs are fully combined and frothy.

Place a large skillet over medium heat and add 2 tablespoons of butter, allowing it to melt and bubble gently.

While the butter is melting, take your bread slices and butter one side of each with the remaining tablespoon of butter. This creates a deliciously crispy exterior for your Egg and Ham Breakfast Sandwich.

Pour the prepared egg mixture into the skillet, instantly swirling it around to achieve an even distribution. Place the buttered bread slices, butter-side-up, right on top of the eggs. Cook for approximately 5-7 minutes.

Once the eggs are set, carefully flip the sandwich using a spatula. On one slice, layer your choice of cheddar cheese and deli ham, then fold the excess egg over the filling. Top it off with the other slice of bread.

Gently flip the sandwich once more and let it cook for an additional 2-3 minutes, until the cheese melts beautifully and the bread turns golden brown.