Try to implement HTTP2 client in Elixir.

http2_study_client.ex

defmodule Http2StudyClient do
  @moduledoc """
  http2study
  """

  @doc "GET HTTP/2.0"
  def get domain, port do
    {:ok, sock} = :gen_tcp.connect domain, port, [:binary, {:packet, 0}]
    try do
      {:ok, data} = send_connection_preface sock
      IO.inspect data
      {:ok, data} = establish_connection sock
      IO.inspect data
      {:ok, data} = send_get_request sock
      IO.inspect data
      :ok = send_goaway sock
    after
      :ok = :gen_tcp.close sock
    end
  end

  defp establish_connection sock do
    {:ok, data} = send_settings sock
    IO.inspect data
    unless data = build_frame(0x01, 0, 0, <<>>) do
      {:error, "Can't establish a connection."}
    else
      send_ack sock
    end
  end

  defp send_connection_preface sock do
    IO.puts "Sending connection preface"
    :gen_tcp.send sock, "PRI * HTTP/2.0\r\n\r\nSM\r\n\r\n"
    case do_receive_once(sock) do
      {:ok, data} ->
        if Regex.match?(~r/^HTTP\//, data) do
          {:error, "not supported."}
        else
          {:ok, data}
        end
      x -> x
    end
  end

  defp send_settings sock do
    IO.puts "Sending SETTINGS"
    :gen_tcp.send sock, build_frame(0x4, 0, 0, <<>>)
    do_receive_once sock
  end

  defp send_ack sock do
    IO.puts "Sending ACK"
    :gen_tcp.send sock, build_frame(0x01, 0, 0, <<>>)
    do_receive_once sock
  end

  defp send_goaway sock do
    IO.puts "Sending GOAWAY"
    no_error = 0
    :gen_tcp.send sock, build_frame(0x7, 0, 0, <<no_error::32>>)
    :gen_tcp.close sock
  end

  defp send_get_request sock do
    IO.puts "Sending GET request"
    end_headers = 0x4
    :gen_tcp.send sock, build_frame(0x1, end_headers, 1, <<
      <<0::1, 0::1, 0::1, 1::1, 0::4, 0::1, size("scheme")::7, "scheme", 0::1, size("http")::7, "http">>,
      <<0::1, 0::1, 0::1, 1::1, 0::4, 0::1, size("authority")::7, "authority", 0::1, size("nghttp2.org")::7, "nghttp2.org">>,
      <<0::1, 0::1, 0::1, 1::1, 0::4, 0::1, size("path")::7, "path", 0::1, size("/")::7, "/">>,
      <<0::1, 0::1, 0::1, 1::1, 0::4, 0::1, size("method")::7, "method", 0::1, size("GET")::7, "GET">>
    >>)
    do_receive_once sock
  end

  defp build_frame frame_type, flags, stream_id, payload do
    header = <<0::2, size(payload)::14, frame_type::8, flags::8, 0::1, stream_id::31>>
    <<header::binary, payload::binary>>
  end

  defp do_receive_once sock do
    receive do
      {:tcp, sock, bin} ->
        <<0::2, payload_size::14, frame_type::8, flags::8, 0::1, stream_id::31, payload::binary>> = bin
        case frame_type do
          0x3 ->
            <<error_code::32, _::binary>> = payload
            {:error, "RST_STREAM error_code:#{error_code}"}
          0x7 ->
            <<error_code::32, _::binary>> = payload
            {:error, "GOAWAY error_code:#{error_code}"}
          _ ->
            {:ok, bin}
        end
      {:tcp_closed, sock} ->
        {:error, "closed."}
      {:tcp_error, sock, reason} ->
        {:error, reason}
    after
      5000 ->
        {:error, "timeout."}
    end
  end

  # defp do_receive_response sock, header \\ [], body \\ [] do
  # end
end

Http2StudyClient.get 'nghttp2.org', 80

Does it work?