How to configure Varnish to conditionally ignore cookie based on Vary response header?

Question

I'm using Varnish 3 for caching responses from a web application that uses Edge Side Includes (ESI).

There are generally two types of responses from ESI endpoints:

• some are authentication-specific, responses thus use Vary: Cookie, Accept-Encoding
• some be cached for all users regardless of cookies, thus responding with Vary: Accept-Encoding (without varying by cookie)

All requests do contain a Cookie header with various cookies. Requests with no Cookie header are responded to with Set-Cookie. Note that this is not the case of __-prefixed cookies from e.g. Google Analytics - these are cookies set by a legacy application, and I have no means to change this behavior.

Is there a way* to configure Varnish 3 to remember that responses from respective ESI endpoints do not vary by cookie, thus future requests should ignore the Cookie header altogether and use a cached response instead of fetching a new one from the backend?

(*) other than hardcoding URIs into Varnish config, i.e. I'm looking for a way for Varnish to respect cookie-less Vary header for requests that do contain cookies.