mix eggs and milk in the bowl with the fork until well mixed

place one pat of butter and ham in one pan and turn on medium heat mixing occasionally

place one pat of butter in other pan and let melt over medium heat

pour eggs into the pan with no ham and cover watching until top of eggs are mostly cooked

flip eggs carefully and turn off heat

immediately add shredded cheese and most of the ham but save some ham for the top

flip eggs in half, plate, and top with more cheese and ham