1. Blend chili-seasoning mix, tomato sauce, water, corn and liquid and ham in a medium-size saucepan; bring to boiling, then simmer, stirring the mixture several times, for 15 minutes.
2. While the sauce simmers, beat eggs with milk until foamy in a medium-size bowl; stir in cheese.
3. Melt butter or margarine over low heat in a medium-size skillet, tipping pan to coat sides; pour in egg mixture.
4. Cook very slowly, stirring gently from bottom and sides of pan, just until the eggs start to set and are creamy-soft; remove from the heat.
5. Spoon chili-ham mixture into a shallow serving dish; mound eggs on top. Garnish with green-pepper rings, if you wish.