There is no configuration for the REST API. It just is and what it provides is what you get.
In OH 3.2 I don’t think there is any option, certainly no official option. There is a REST API but you have to use POST to send a command to an Item and PUT to post and update to an Item. You can get more details in MainUI under Developer Tools API Explorer.
In OH 4 there is a Webhook binding you can install from the marketplace. Webhook HTTP binding
In OH 5 I think they are adding a webhook REST endpoint that lets you send commands or update an Item using HTTP GET.
There used to be an unofficial and unsupported hack using BasicUI, but I don’t remember when that stopped working and since it’s years since I last touched OH 3 I don’t have anywhere to look.