- 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.