sub { $midi_indev = $midi_outdev; ...}

##</code><code>##

my $midi_outdev_ref = \$midi_outdev;
...
    -variable => $midi_outdev_ref,
    ...
    sub { my $midi_indev = $$midi_outdev_ref; ... },
    ...

##</code><code>##

#!/usr/bin/env perl

use strict;
use warnings;

use Tk;
use Tk::BrowseEntry;

my @choices = 'A' .. 'Z';
my $picked = $choices[0];
my $picked_ref = \$picked;

my $mw = MainWindow::->new();

$mw->BrowseEntry(
    -variable => $picked_ref,
    -choices => \@choices,
)->pack();

$mw->Button(
    -text => 'Print Choice',
    -command => sub {
        print "Choice: $$picked_ref\n";
    },
)->pack();

MainLoop();