Take a look at the test suite, in t/06_long_resp.t there is the approach on how to generate a response using multiple callbacks:

$h->reg_cb (
   '/test' => sub {
      my ($httpd, $req) = @_;
      $req->respond ({
         content => ['text/plain', sub {
            my ($data_cb) = @_;
            return unless $data_cb;
            $data_cb->(substr $SENT, 0, 10, '');
         }]
      });
   },
);
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Basically, it is the same approach that Plack uses. Your ->respond call passes in a subroutine, that gets another callback as a parameter. You then call this callback every time you have more content for the response.