Slice the tops off the tomatoes, keeping the tops and the stems intact. Scoop the insides of the tomato out, and dry the inside of each tomato with paper towel.
Evenly distribute the corn, peas, ham and cheddar cheese between the tomatoes.
In a small bowl, mix together the eggs, milk, salt, pepper and nutmeg.
Place the tomatoes and their tops on a baking sheet lined with parchment paper, and the pour the egg mixture into the tomatoes. Bake at 350F for 20-25 minutes until the egg has fully cooked and is golden brown.