In a large skillet, saute the sliced brat rings with the diced bell pepper and broccoli florets. Cook for 5-7 minutes until warmed throughout and veggies are crisp-tender.
Place the veggie mixture into a bowl and cover it while you prepare the eggs.
Whisk together 2 eggs with 1/8 cup milk. Add in a pinch of salt and pepper, and dry mustard. Stir.
Grease the same skillet and heat over medium heat. Put a drop of egg mixture into the skillet, and if it cooks right away, you are ready to pour the eggs into the pan.
Pour in the egg mixture and allow the eggs to cook for 1 minute. Using a spatula, scramble up the eggs as they continue to cook.
After 2 - 3 minutes of cooking, when eggs are set, add in the veggie/brat mixture.
Remove from heat, and top the dish with cheese.