JSESSIONID Cookie with Expiration Date in Tomcat

Question

What's the best way to set an expiration date for the JSESSIONID cookie sent by Tomcat for a servlet session?

By default, the expiration date of the cookie seems to be 'session', which means that the session disappears in the client as soon as the browser restarts. But I would like to keep it open for 12h, even after a browser restart (and would then configure the session timeout in the server accordingly).

Is there any way to set an expiration date within Tomcat, e.g. using some configuration option or extension module? Or is there a reliable way to set an expiration date for JSESSIONID using a Servlet filter?