If you’re taking the web out of the equation, Exercism’s elixir track is a good place to start. They’re not more complete projects in the way I think of those, like the weather station one mentioned earlier but the exercises are a good slow progression beyond the basics.
As a beginner, I found Elixir koans to be another good introduction to the language. The compiler error messages almost give you the answer sometimes but you can run through them very quickly. For me, they helped solidify the topics I covered in the docs.
