>perl -wMstrict -le
"my $open  = '{{';
 my $close = ']]';
 ;;
 my $opener = qr{ \Q$open\E  }xms;
 my $closer = qr{ \Q$close\E }xms;
 my $body   = qr{ [^\Q$open$close\E] }xms;
 ;;
 my $regex = qr{
     (
     $opener
     (?:
     $body++
     |
     (?1)
     )*
     $closer
     )
     }xms;
 ;;
 my $s = 'xxx {{ foo {{ bar ]] baz ]] yyy {{ fee ]] zzz';
 ;;
 print qq{'$1'} while $s =~ m{ $regex }xmsg;
"
'{{ foo {{ bar ]] baz ]]'
'{{ fee ]]'

##</code><code>##

>perl -wMstrict -le
"print qq{perl version $]};
 ;;
 my $opener = qr{ \{\{ }xms;
 my $closer = qr{ \]\] }xms;
 my $body   = qr{ (?! $opener) (?! $closer) . }xms;
 ;;
 use re 'eval';
 our $regex = qr{
   $opener
   (?: (?> $body+) | (??{ $regex }) )*
   $closer
   }xms;
 ;;
 my $s =
   'xxx {{ foo {{ bar ]] baz [OK] ]] [NO] yyy {{ fee ]] zzz';
 ;;
 print qq{'$1'} while $s =~ m{ ($regex) }xmsg;
"
perl version 5.008009
'{{ foo {{ bar ]] baz [OK] ]]'
'{{ fee ]]'