Whisk together the eggs and milk in a large measuring cup or bowl.

Heat a non stick skillet over low heat. Melt a tablespoon of butter in the skillet. Add the eggs and allow to cook undisturbed for about 30 seconds. Then, drag a rubber spatula through the egg mixture and around the edges to allow uncooked portions to hit the skillet. Continue to drag and scrape the spatula every 10-15 seconds until the eggs are in curds. Remove from heat when the eggs still look slightly “wet.”

Season to taste with salt and pepper and snipped chives, then divide the eggs into equal portions for the sandwiches, draping a slice of cheese over each one so it can melt.

Meanwhile, toast the bread (if desired). To assemble the sandwiches, spread mayonnaise and a dollop of dijon mustard on the inside of both sides of the bread. Top one slice with lettuce and sliced tomato, seasoning the tomato with a pinch of salt and pepper. Add eggs and top with the second slice of bread.