Separate egg yolks fro egg whites.
Mix egg yolk, mayonnaise, mustard, salt, pepper, chili powder until very smooth. I use a small food processor for this, but you don't have to.
Chop egg whites and cheddar cheese into small pieces. You can also use shredded cheddar, but it doesn't usually have as much flavor.
Arrange on lettuce, add dash of paprika.