$ cat 1004138.pl 
#!/usr/bin/perl
use strict;
use warnings;
use 5.10.0;
use autodie;

my $filespec = "abc*.xml";
my @dirs = ('ABC');

while (@dirs) {
    my $curdir = pop @dirs;
    opendir(my $dh, $curdir);
    for my $f (readdir($dh)) {
        next if $f =~ /^\.\.?$/;
        next unless -d "$curdir/$f";
        print "pushing $curdir/$f\n";
        push @dirs, "$curdir/$f";
    }

    for (glob("$curdir/$filespec")) {
        print "processing $_\n";
    }
}

$ perl 1004138.pl
pushing ABC/DEF
pushing ABC/GHI
pushing ABC/JKL
processing ABC/abcde.xml
processing ABC/JKL/abc_x.xml
processing ABC/JKL/abc_y.xml
processing ABC/JKL/abc_z.xml
pushing ABC/GHI/baz
pushing ABC/GHI/foo
pushing ABC/GHI/bar
processing ABC/GHI/abc_5.xml
processing ABC/GHI/abc_6.xml
processing ABC/GHI/bar/abc_1.xml
processing ABC/GHI/bar/abc_2.xml
processing ABC/GHI/bar/abc_3.xml
processing ABC/GHI/bar/abc_4.xml
processing ABC/GHI/foo/abc_8.xml
processing ABC/GHI/foo/abc_9.xml
processing ABC/GHI/foo/abc_a.xml
processing ABC/GHI/foo/abc_b.xml
processing ABC/GHI/baz/abc_{7}.xml