This is simple but I keep needing to look it up.

First check your elixir version:

elixir -v

Second confirm that you actually installed Elixir using brew:

brew list | grep elixir

Third do the upgrade:

brew upgrade elixir

Note: You are probably going to find more than just elixir itself is upgraded. Theoretically you should be able to look at just the upgrade tree with:

brew deps --tree --include-build elixir

and only those things will be upgraded but when I noted a much larger group of packages being upgraded which makes me suspect some kind of circular dependency that needed to be handled.

Fourth check the version again:

elixir -v