Off the top of my head, it might be worth trying to pass in conn without using the capture operator. Also, check out these other requirements from the Plug.Router docs:

Each route receives a conn variable containing a Plug.Conn struct and it needs to return a connection, as per the Plug spec…
Each Plug.Router has a plug pipeline, defined by Plug.Builder, and by default it requires two plugs: :match and :dispatch. ``

So maybe something like this for a minimal example using only Plug.Router:

defmodule AppRouter do
  use Plug.Router

  plug :match # required by default
  plug :dispatch # required by default

  get "/baz" do
    HelloWorld.Controller.show(conn) # must accept and return a connection
  end
end