Mix your eggs, milk, salt and pepper in a small bowl with a whisk or fork.
Add butter in a small pan (I recommend 8 inch pan) over medium high heat.
Once butter is melted and sizzling, add your egg mixture.
Continue to heat for a few minutes until egg mixture is no longer runny, but now firm. This usually takes 4-5 minutes.
Sprinkle a little bit of cheddar cheese on one side of the omelette. Add in your vegetables. Top with another sprinkle of cheese.
Once no longer runny, carefully use a spatula to fold up omelette, so that one side goes on top of your vegetables.
Using the spatula, gently press down omelette and continue to cook for 1 more minute.
Serve warm, enjoy!