<?php

$arr = [
  'vehicle info' => [
     'one' => ['submodel' => 'LX', 'engine' => '2.3'],
     'two' => ['color' => 'blue', 'year' => '2007', 'wheels' => '4'],
     'three' => ['submodel' => 'LX', 'make' => 'Ford', 'model' => 'F-150', 'offroad' => 'No'],
    ],
];

function find($needle, $haystack, $found = '')
{
    foreach ($haystack as $key => $value) {
        if ($found) {
            break;
        }
        if ($key === $needle) {
            $found = "{$needle} is {$value}";
            break;
        }
        if (is_array($value)) {
            $found = find($needle, $value, $found);
        }
    }
    return $found;
}

$wanted = 'submodel';
$result = find($wanted, $arr);

var_dump($result);