Place the eggs in a bowl and beat until well blended; season with salt and pepper. Lightly vegetable spray a large non-stick skillet and set over medium heat. Add the eggs.
As the eggs begin to set on the bottom, gently move a heatproof spatula across the bottom and sides of the skillet to form large, soft curds. Continue cooking until the eggs are cooked, but still moist, and then remove from the heat.
While still warm, divide and shape the eggs into six, round servings each the width of an English muffin. Cool eggs to room temperature.
Spread the cut sides of each muffin lightly with butter (or margarine). Sandwich a portion of egg, slice of cheese and your desired accents into each muffin. Individually wrap, label and date each sandwich and set on a baking sheet. Freeze the sandwiches until solid then transfer to a freezer bag until needed.
To heat, unwrap and set a frozen egg sandwich on a plate. Place the plate in the microwave and tent with a piece of parchment paper or paper towel. Cook the sandwich on high in 30 seconds spurts, until heated through. That should take about 90 to 120 seconds.
Options: Beyond egg and cheese, you could also accent these breakfast sandwiches with one or more other tastes. Items that would work are sliced Canadian bacon, crisply cooked regular bacon, sliced ham, tomato salsa, and sliced and sautéed onions and bell peppers.