Whisk together eggs, milk, and chives, then season with salt and pepper.
In a medium pan at medium heat melt the butter, then pour half of the egg mixture into the pan, so that it covers the entire pan, and cook for 2 minutes.
Add half of the shredded cheddar and cover for 2 minutes more, until the cheese is melty. Remove onto plate, add 2 slices of ham on top and roll tightly, then cut in bite-size pieces. Repeat with the remaining ingredients.
Serve with mixed salad or cut raw vegetables