Formatting PHP Function Returns

Person I have the following database structure:

id | parent_id | username

Where a parent can have n children and these children generate n children, this structure is already working, what I need is an example output:

[
    (int) 1 => 'User1 ',
    (int) 2 => 'User1 > User2 ',
    (int) 3 => 'User1 > User3 ',
    (int) 4 => 'User3 > User4'
    ....
]

From it I can generate a Select in my application. The code below is working, it already does much of what I need except the

  

mountMenuArrayList (array $ menuTotal, $ parent_id, array $ new = null)

I need it to output the array above, but it only generates the first two values

[
   (int) 2 => 'User2 ',
   (int) 3 => 'User2 > User3 '
]

My Input Array:

[
    (int) 1 => [
        (int) 2 => [
            'id' => '2',
            'parent_id' => '1',
            'username' => 'User2'
        ],
        (int) 10 => [
            'id' => '10',
            'parent_id' => '1',
            'username' => 'User10'
        ]
    ],
    (int) 2 => [
        (int) 3 => [
            'id' => '3',
            'parent_id' => '2',
            'username' => 'User3'
        ],
        (int) 4 => [
            'id' => '4',
            'parent_id' => '2',
            'username' => 'User4'
        ]
    ],
    (int) 10 => [
        (int) 11 => [
            'id' => '11',
            'parent_id' => '10',
            'username' => 'User11'
        ],
        (int) 12 => [
            'id' => '12',
            'parent_id' => '10',
            'username' => 'User12'
        ]
    ],
    ....
]

What I need in the end is that the output is an array with this structure and should be done by the function montaMenuArrayList ():

[
    (int) 1 => 'User1 ',
    (int) 2 => 'User1 > User2 ',
    (int) 3 => 'User1 > User3 ',
    (int) 4 => 'User3 > User4'
    ....
]

My Current Code:

    public function criaArvoreRev($arvoreCompleta)
    {
        foreach($arvoreCompleta as $key => $rev){
            $arvore[] = $this->organizaArvoreRev($arvoreCompleta, $rev['id']);
        }
        return $arvore;
    }        

    public function organizaArvoreRev($revTotal, $parent_id = null)
    {
        $menuItem = [];
        foreach ($revTotal as $user){
                if(!empty($user) && ($user['parent_id'] == $parent_id || $user['id'] == $parent_id)){
                    $menuItem[$user['id']] = ['id' => $user['id'], 'parent_id' => $user['parent_id'], 'username' => $user['username']];
                }
            }
        return $menuItem;
    }


    public function nivelArray(array $array)
    {
        $newArray = array();

        foreach($array as $key => $val){
            if( isset($val['id']) ){
                $parent_id = $val["parent_id"];
                $id = $val["id"];
                $newArray[$parent_id][$id] = ['id' => $val["id"], 'parent_id' => $val["parent_id"], 'username' => $val["username"]];
            }else{
                foreach($val as $k => $v ){
                    $parent_id = $v["parent_id"];
                    $id = $v["id"];
                    $newArray[$parent_id][$id] = $v;
                }
            }
        }
        return $newArray;
    }

    public function encontraRev(array $arvore, $id, $newline = null)
    {
        foreach($arvore as $key => $rev){            
            if(array_key_exists($id, $rev)){
                $newline =  $rev[$id]['username'] . " > " . $newline;
                if($key == 1) unset($arvore[$key][1]);
                return $this->encontraRev($arvore, $rev[$id]['parent_id'], $newline);
            }
        }
        return $newline;
    }

    public function montaMenuArrayList( array $menuTotal , $parent_id, array $new = null )
    {
        foreach($menuTotal[$parent_id] as $key => $val)
        {
            $id = $key;
            $valor_display = $this->encontraRev($menuTotal, $id);
            $valor_display = substr($valor_display, 0, -2);
            if($key == 1) unset($menuTotal[$key][1]);
            if( isset( $menuTotal[$key] ) ){
                $new[$id] = $valor_display; 
                return $this->montaMenuArrayList($menuTotal, $id, $new);
            }    
        }

        return $new;
    }