How to have a 'connectedCallback' for when all child custom elements have been connected

I'm using Web Components v1.

Suppose two Custom Elements:

parent-element.html

<template id="parent-element">
    <child-element></child-element>
</template>

child-element.html

<template id="child-element">
<!-- some markup here -->
</template>

I'm trying to use connectedCallback in parent-element to initialise the entire parent/child DOM structure when it is attached, which requires interaction with methods defined in child-element.

However, it seems child-element isn't properly defined at the time connectedCallback gets fired for customElement:

parent-element.js

class parent_element extends HTMLElement {
    connectedCallback() {
        //shadow root created from template in constructor previously
        var el = this.shadow_root.querySelector("child-element");
        el.my_method();
    }
}

This will not work, because el is an HTMLElement and not a child-element as expected.

I need a callback for parent-element once all child custom elements in its template have been properly attached.

The solution in this question does not seem to work; this.parentElement is null inside child-elementconnectedCallback().

ilmiont