I want variable substitution in part of the command.

So just escape those dollars which you want to pass as literals.

#!/usr/bin/env perl 
use strict;
use warnings;
use Test::More tests => 1;

my $boot_device = '/dev/md126p1';
my $cmd = qq#blkid $boot_device | awk '{ print \$2 }' | sed 's/"//g'#;
my $shouldbe = q#blkid /dev/md126p1 | awk '{ print $2 }' | sed 's/"//g
+'#;
is ($cmd, $shouldbe);
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And never pipe awk to sed - that would be pointless.