After looking at framework's implementation of HttpCookieCollection again, it's actually just a collection that gets written at the end. I've updated this to do the same by hooking into the HttpResponse.OnStarting event.

I've also added a couple of endpoints that manipulate cookies and they do it the same now on framework and core.

This will not keep the worlds in-sync (i.e. cookies set by using the adapters with the cookies set using IResponseCookies). However, this is similar to ASP.NET framework where if you're working directly with the header, things wouldn't show up there either.