In a small microwave-safe bowl, microwave the butter until melted, for about 30 seconds. Brush it all over the bowl.
Break the eggs into the bowl. Add the milk, salt, and pepper.
Whisk to combine.
Microwave the eggs, uncovered, for 45 seconds.
Gently stir the eggs with a fork, then stir in the cheese, if using.
Microwave until fluffy and set but not completely dry, about 45 more seconds. Serve immediately.
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Notes
You lose some amount of control when using the microwave. Cooking on the stove lets you cook low and slow, ensuring fluffy and moist eggs. Microwave eggs can end up too dry if you're not careful. So it's best to slightly undercook than to overcook them. Remember, you leave them in a hot mug or bowl after they're done cooking; they will continue to cook after you remove them from the microwave. You can always add 10 more seconds in the microwave if they are too moist for your liking.
This recipe was written for the average microwave wattage, around 1,000. If your microwave's wattage differs, experiment with how long to cook the eggs and at what power level.
If the eggs are fully cooked, you can keep the leftovers in the fridge, in an airtight container, for up to 4 days. Reheat them gently, covered, in the microwave at 50% power. I don't recommend freezing these eggs.