haproxy.cfg

global
	log /dev/log	local0
	log /dev/log	local1 notice
	chroot /var/lib/haproxy
	stats socket /run/haproxy/admin.sock mode 660 level admin
	stats timeout 30s
	user haproxy
	group haproxy
	daemon

	# Default SSL material locations
	ca-base /etc/ssl/certs
	crt-base /etc/ssl/private

	# Default ciphers to use on SSL-enabled listening sockets.
	# For more information, see ciphers(1SSL). This list is from:
	#  https://hynek.me/articles/hardening-your-web-servers-ssl-ciphers/
	ssl-default-bind-ciphers ECDH+AESGCM:DH+AESGCM:ECDH+AES256:DH+AES256:ECDH+AES128:DH+AES:ECDH+3DES:DH+3DES:RSA+AESGCM:RSA+AES:RSA+3DES:!aNULL:!MD5:!DSS
	ssl-default-bind-options no-sslv3

defaults
	log	global
	mode	http
	option	httplog
	option	dontlognull
        timeout connect 5000
        timeout client  50000
        timeout server  50000
	errorfile 400 /etc/haproxy/errors/400.http
	errorfile 403 /etc/haproxy/errors/403.http
	errorfile 408 /etc/haproxy/errors/408.http
	errorfile 500 /etc/haproxy/errors/500.http
	errorfile 502 /etc/haproxy/errors/502.http
	errorfile 503 /etc/haproxy/errors/503.http
	errorfile 504 /etc/haproxy/errors/504.http

frontend www-https
    bind env(HAPROXY_IP):443 ssl crt /etc/ssl/private/my_cert_and_key.pem
    reqadd X-Forwarded-Proto:\ https
    default_backend www-backend

backend www-backend
   server www-1 env(HOME_ASSISTANT_IP):8123 check

listen stats *:1936
    stats enable
    stats uri /
    stats hide-version
    stats auth HAPROXY_USER:HAPROXY_PASS

Hi!
Does it work properly?
I still didn't add a SSL encryption, but I mad proxing to hass through haproxy and hass frontend shows:

So I little confused that it works on your system. If you r interested and have some time - I can share my config and logs.

Yes it worked for me. I've changed the gist for a resin Dockerfile I'm making now though. If you need my help ping me in the home-assistant channel on gitter.