Yeah, I didn't check in before just trying this so I missed that you'd solved it. I'll leave some code for future readers. The docs are thin so I'm not surprised you didn't get it right the first time.

# in MyApp.pm
__PACKAGE__->config(
          "Plugin::Cache" => {
              backend => {
                  class  => "Cache::MemoryCache",
              }
          });

# in MyApp::Controller::Root
sub counter :Local Args(0) {
    my ( $self, $c ) = @_;
    my $counter = $c->cache->get("counter") + 1;
    $c->cache->set( counter => $counter );
    $c->response->body("Count #" . $counter);
}
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Sounds like you already figured out the other parts like expiration. Have fun and realize these are volatile and if I read the docs right they share data or don't depending on the engine the app is running.