How to get an Entry in structure and all of its children and it's children's children with Element APi?

Question

How do I get all of an entry's children using the Element API?

I want to return something like:

data: [
    title: 'Root Entry'
    uri: 'root-entry'
    children: [
        {
            title: 'Level 2 Entry'
            uri: 'level-2-entry-1'
            children: [
                {
                    title: 'Level 3 Entry'
                    uri: 'level-3-entry'
                    children: [...]
                },
            ]
        },
        {
            title: 'Level 2 Entry'
            uri: 'level-2-entry-2'
            children: [...]
        },
        {
            title: 'Level 2 Entry'
            uri: 'level-2-entry-3'
            children: [...]
        },
    ]
]

I would want to get all entries up to the depth level of 4. Some entries wont have children past level 3 and some wont have any past level 2. I have tried doing a for loop traversal but cannot figure out why $entry->children returns everything but children entries.