WP function to display custom taxonomies in WP-Admin Style?

I have added a custom taxonomy to Users – user categories.

Using the code below, I am able to output the custom taxonomies in each edit-user profile page:

function show_user_category( $user ) {

//get the terms that the user is assigned to
$assigned_terms = wp_get_object_terms( $user->ID, 'user_category' );
$assigned_term_ids = array();
foreach( $assigned_terms as $term ) {
    $assigned_term_ids[] = $term->term_id;
}

//get all the terms we have
$user_cats = get_terms( 'user_category', array('hide_empty'=>false) );

echo "<h3>User Category</h3>";

//list the terms as checkbox, make sure the assigned terms are checked
foreach( $user_cats as $cat ) { ?>
    <input type="checkbox" id="user-category-<?php echo $cat->term_id ?>" <?php if(in_array( $cat->term_id, $assigned_term_ids )) echo 'checked=checked';?> name="user_category[]"  value="<?php echo $cat->term_id;?>"/>
    <?php
    echo '<label for="user-category-'.$cat->term_id.'">'.$cat->name.'</label>';
    echo '<br />';
}
}

The code above simply displays a list of checkboxes, ordered by term_id.

Of course, I want to display them in the same way that custom taxonomy terms would be displayed in a custom post type (a scrollable list of checkboxes, with child terms indented and underneath their parent term). The code above does not display the terms in order of parents/children.

Is there a WP function I can pass my taxonomy & terms to, to create what I described in the paragraph above? Or do I have to do it manually?

Thanks