В общем перечитал APIшку и решение было следующим
$token = 'TOKEN';
$apiUrl = 'https://api.monday.com/v2';
$headers = ['Content-Type: application/json', 'Authorization: ' . $token];
$query = 'mutation{ create_item (board_id:id, group_id: "group", item_name:"name") { id } }';
$data = @file_get_contents($apiUrl, false, stream_context_create([
'http' => [
'method' => 'POST',
'header' => $headers,
'content' => json_encode(['query' => $query]),
]
]));
$responseContent = json_decode($data, true);
echo json_encode($responseContent);