I love chipped beef because we learned to prepare it properly and from scratch when I was a kid. The military gave chipped beef a bad name because they don't do either of those things well and they use crumbled ground beef, not chipped dried beef. Stauffer's isn't a bad product but at $4.99 it's pricey, portions are small, and it's way too salty. If you've never had home-made chipped beef, you can't really know how good it is. Here's how to do it right.
I start with what they used to call the "white sauce", which I believe can actually be a complicated and fussy double boiler affair, but in this household, this is just flour and milk in a generously buttered large fry pan on low heat. I start with 1/4 cup of flour and gradually stir in the milk, working out any lumps as we do with gravies. If you add the milk slowly and stir to a uniform thickness before adding more, you don't get lumps, so you probably save time anyway.
It's worth noting that my mom would just mix all the ingredients in the milk and heat it, adding flour as she went. I am not that good and always got lumpy sauces, and I heard about it, too.
The quarter cup of flour turned out to be exactly right, and I believe I ended up using about 1/3 quart of milk, but you are going for a medium sauce consistency. Remember it thickens some more after you turn off the heat.
Now that the "easy sauce" is done my way:
Slice the hard boiled eggs and add to the sauce. Separate out the thin beef shavings and rinse in lukewarm water to remove excess salt. Add to the sauce and eggs, and stir until eggs are beef are warm.
Serve immediately over toast. Season with paprika and/or ground black pepper.