If it's a RESTful API purely for transferring data and not for making nice UIs like Swagger does (which you can use with Spring MVC btw), I would suggest the following options:
Vert.X - I've just written an API in Vert.X and it's lightning fast, it's reactive and you can have many thousands of concurrent connections. Startup time is around 10 milliseconds. Also, you don't need a container for it, it opens up its own port and accepts connections directly without the need for Tomcat or Jetty. Furthermore, the response times I'm getting on requests is much faster than anything I've seen before. API feels a bit barebone, but it's all you need.
To get routing out of the box, you'll need VertX Web, VertX + VertX Web is literally all you need to easily handle REST requests whether you're doing CORS, or secure cookies, PUT, POST, GET, DELETE, OPTIONS, custome headers, etc.
If you're going the route of Jersey or JaxRS, combine it with the Comsat Stack which will effectively inject a Java Agent into your Jetty / Tomcat which wil replace the one-thread-per-request with one-fiber-per-request - fibers (or Quasars) are super lightweight threads which should give you the same performance as Vert.X does, but with a slightly more refined API to work with and allows you to write synchronous blocking code and having it handled in a reactive way.
If you're not looking for something super high-tech and something that is very well documented so that anyone on the team can instantly find answers, that would be Spring MVC combined with Gson or Jackson if you're using JSON as interchange format. (I just noticed Comsat is now available for SpringMVC as well )
Grizzly has been built on top of NIO, I don't know if they have plans to incorporate NIO2 and I can't comment on the performance as I haven't used it myself.
Alternatively, you can go super low level and use Servlets directly - I believe you can combine it with RxJava to get it more reactive, but I haven't done this myself.
If you don't mind mixing some Kotlin into your application (Kotlin interoperates with Java 100%), you can also check out Kovert which is just as bare-bone as Vert.X, or alternatively kottpd which feels very similar to Vert.X in terms of how it is self-contained, but only caters for the bare-basics.
Retrofit as well as Fuel are recommended in the Kotlin in Action book, although I haven't had time to look at them in depth.
Undertow and Netty I keep on seeing in benchmarks , but you might need to get your hands dirty to write your own RESTful server on top of it.