Sorting on Nested Element

[dsb]

Hello all, I'm trying to sort on a nested key value. Given a data structure that looks like this:

$data = { Elements => {
    AlphaKey => {
        Name => 'Foo',
        Priority => 2,
        OtherVal => 'randomthings'
    },
    BetaKey => {
        Name => 'Bar',
        Priority => 1,
        OtherVal => 'morerandomthings'
    },
}};

I want to process them in a sorted order based on the priority value. I'm trying to just turn the hashref into an arrayref, so that it winds up looking like:

$sorted = [
    {
        Name => 'Bar',
        Priority => 1
        OtherVal => 'morerandomthings'
    },
    {
        Name => 'Foo',
        Priority => 2,
        OtherVal => 'randomthings'
    },
];

It's easy enough to get a sorted list of priorities:

my @pri = sort { $a <=> $b } map { $data->{Elements}{$_}->{priority} }
+ keys %{$data->{Elements}};

I'm lost on how to build an arrayref-based structure from there. I'm not even sure i'm going down the right path now that I'm typing it out. Thoughts?