use warnings;
use strict;
use 5.012;

my $data = <<'END_OF_TEXT';
foo
bar
{{
alpha
beta
}}
baz
END_OF_TEXT


$data =~ s/
    (?:          #Non-capturing group
        {{.*?}}  #Text enclosed by double braces
        \K       #Exclude what's to the left of \K from match
    )?           #Match whole group 0 or 1 time
    \n
/\n<br>/gxms;


say $data;

--output:--
foo
<br>bar
<br>{{
alpha
beta
}}
<br>baz
<br>