How to obtain a request verification token cookie using HttpClient?

When my browser does a get request for this site, the request obtains a request verification token as a cookie from the server and adds it to the header of the get request. There's a picture of the cookie in question from the Chrome network tab.

This cookie/token expires when the browsing session ends. How can I use an HttpClient to obtain this token and add it as a cookie to my headers for a post request?
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