Melt the butter in a large skillet over medium heat.
In a small bowl, whisk together the eggs and milk until fully combined.
Pour the egg mixture into the skillet and let it cook undisturbed for about 30 seconds, just until the edges begin to set.
Add the diced ham, green pepper, tomato, and onion to the skillet. Gently stir to combine and continue cooking for 2 to 3 minutes, stirring occasionally, until the eggs are mostly set but still slightly soft.
Turn off the heat and sprinkle the shredded cheddar cheese over the eggs. Stir gently until the cheese melts and the eggs finish cooking from the residual heat.
Season with salt and pepper to taste and serve hot.
Use Medium Heat: Cooking scrambled eggs over medium heat helps prevent them from drying out or browning too quickly.
Add Mix Ins After the Eggs Start Setting: Letting the eggs cook briefly before adding the ham and vegetables keeps the scramble soft instead of watery.
Do Not Overcook: Turn off the heat while the eggs are still slightly soft. They will finish cooking as the cheese melts.
Drain Juicy Ingredients: If your tomatoes are very juicy, pat them dry before adding to avoid excess moisture in the eggs.
Serve Immediately: Scrambled eggs are best enjoyed fresh while they are soft and fluffy.