Mix the mustard, half and half, onion powder, garlic powder, salt and pepper together in a small bowl. Crack the 6 eggs into a medium-sized bowl and spoon in the mustard mixture; whisk lightly. Slowly whisk in the cheese.

Melt butter in a medium frying pan and add the ham.  Cook for about 2-3 minutes to warm ham before adding the egg mixture. With the heat on medium-low, add the egg mixture to the skillet and immediately start moving the eggs around the pan with a spatula. Cook the eggs on a lower heat.

Cook until eggs are cooked through and slightly firm yet a bit creamy. Enjoy those breakfast eggs!