This Burp extension extracts all the values a particular cookie is set to, using data from the Proxy History.
To use it, right-click on a request that contains the cookie you're interested in, in the Proxy History table. The pop-up context menu will includes Extract Cookie Values and a sub menu lets you pick the relevant cookie. The values will be extracted from all the Set-Cookie headers and you will be prompted for a file name to save these into.