@nnicola What you’re describing is basically a proxy. Your 15 sites make a request to your proxy, and your proxy either forwards the request on to the end API, or returns a previously-cached response if appropriate.
I wouldn’t use Laravel for this because using a full-stack framework just for the sake of forwarding a HTTP request seems overkill. AWS has an API gateway service that’s imaginatively called API Gateway. If the end API uses HTTP cache headers appropriately then the gateway could probably leverage them. If App 1 makes a request and gets a response from the API, then that response could be cached so that when another App calls the same endpoint, they get the response cached from when App 1 made the request, instead of going out to the API again.