In terms of beauty in engineering, do you know what I find to be beautiful?
Well, here's one thing: it's coming up with a plan to secure a particular network protocol, documenting the plan, and then implementing the plan in code that executes in several radically different environments.
It is (perversely?) pleasurable to see seemingly random bytes be transmitted onto a wire from one peer on the network destined to another very different peer on the network and to have all of these bytes be decoded and authenticated properly. The mathematics behind this stuff is extremely pretty, and making it all work in the Real World is fascinating.
The icing on the cake is knowing that all of the code is efficient and scalable, and that the code has a reasonable test harness so that there are no hidden surprises.
As a character on a TV show once said, I love it when a plan comes together.