In a small bowl, whisk together the eggs and milk until the eggs are homogenous with no pockets of egg whites.
Toast the bread over your preferred setting.
Heat a non-stick skillet over low heat and add in 1 tablespoon of butter, then swirl to melt.
Add in the beaten eggs and let cook, undisturbed, for about 20 seconds.
Use a rubber spatula to stir and fold the eggs, so the uncooked parts come into contact with the pan.
Continue stirring and folding every 20 seconds until the eggs start to form curds, are just set, and still appear wet. Remove the pan from the heat.
Season the eggs with salt and pepper to taste, then fold in the chives if using.
Cut the eggs into two equal portions with the spatula, top each portion with one slice of cheese (if using), and let melt.
While the cheese is melting, butter one side of each piece of toast with the remaining tablespoon of butter.
Build the sandwich.
If using greens, place them on the buttered side of the bread, then place the egg and cheese slab on the greens, followed by the rest of the toppings.
Top with the second slice of toast, buttered side down.
Serve warm, and enjoy!