You can use the chunked transfer encoding to write sequentially to the client. Browsers (usually) parse and display the sent data immediately after the first chunk is read.

Update: mod_perl example

package My::Stream;

use strict;
use warnings;
  
use Apache2::RequestRec ();
use Apache2::RequestIO ();
use Apache2::Const -compile => qw( OK );

sub handler :method {

    my $invocant       = shift;
    my $request_record = shift;

    $request_record->content_type( 'text/html' );

    for ( 1 .. 10 ) {
        $request_record->print( "<p>$_</p>" );
        $request_record->rflush;
        sleep 1;
    }

    return Apache2::Const::OK;

}

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