On the TopTal site they've posted a tutorial from author André Castelo showing you how to create a Laravel-based RESTful API with functionality that already exists in the framework.
Laravel is a PHP framework developed with developer productivity in mind. [...] In this article, we’ll explore the ways you can build—and test—a robust API using Laravel with authentication. We’ll be using Laravel 5.4, and all of the code is available for reference on GitHub.
He starts off by talking about RESTful APIs, what actions the HTTP verbs represent and a note about consistency in URLs. He then starts in on the project setup, creating a new Laravel application and configuring the database for a Homestead environment. Next he creates the models and data seeders for articles and users for the API. Routes and controllers come next showing how to work with route model binding and response codes to correctly relay the status of the request back to the user. Following this he covers authentication on the API (using a token) and building out the endpoints for login, registration and logging out.
Finally he shows how to test the endpoints using some simple Laravel-enabled testing and PHPUnit. His tests check things like login error handling, missing data on registration and the correct flow on the logout process.