Cook the diced ham in a hot pan over medium heat, stirring occasionally, until lightly browned. Remove the ham to a bowl, leaving any grease in the pan.
Check the amount of grease in the pan. If cooking the ham left a substantial amount, add butter or oil until you have about 4 tablespoons. If cooking the ham left no grease at all, add all 4 tablespoons of the butter or oil.
Add the flour to the melted butter, oil, or grease, and whisk together until completely mixed and smooth.
Pour in the milk slowly, stirring all the while. Continue to stir until thickened, and then return the ham to the pan.
Reduce the heat to low, and simmer for ten minutes. Taste, and then add up to 1/2 teaspoon and up to 1/2 teaspoon pepper if you like.
Serve over potatoes, biscuits, vegetables, or wrapped up in a tortilla.