The easiest way to add REST server to your vaadin app is to use Javalin in the standalone mode. By default, Javalin runs its own Jetty server. However, your Vaadin app is already running in a servlet container. We can simply exclude Jetty from Javalin dependencies and use Javalin via the regular Servlet API.

Add Javalin to your build script:

    implementation("io.javalin:javalin:4.6.7") {
        exclude(group = "org.eclipse.jetty")
        exclude(group = "org.eclipse.jetty.websocket")
        exclude(group = "com.fasterxml.jackson.core")
    }

Then add the following class to your project:

@WebServlet(name = "MyJavalinServlet", urlPatterns = {"/rest/*"})
public class MyJavalinServlet extends HttpServlet {
    private final JavalinServlet javalin = Javalin.createStandalone()
            .get("/rest", ctx -> ctx.result("Hello!"))
            .javalinServlet();

    @Override
    protected void service(HttpServletRequest req, HttpServletResponse resp) throws ServletException, IOException {
        javalin.service(req, resp);
    }
}

Your servlet container will automatically discover the servlet and initialize it properly. To test, you can run

$ curl -v localhost:8080/rest

Testing: follow this example, to only initialize the REST servlet (no need to initialize the Vaadin servlet as well):

class MyJavalinServletTest {
    private var server: Server? = null

    @BeforeEach
    fun startJetty() {
        val ctx = WebAppContext()
        ctx.baseResource = EmptyResource.INSTANCE
        ctx.addServlet(MyJavalinServlet::class.java, "/rest/*")
        server = Server(30123)
        server!!.handler = ctx
        server!!.start()
    }

    @AfterEach
    fun stopJetty() {
        server?.stop()
    }

    @Test
    fun testRest() {
        assertEquals("Hello!", URL("http://localhost:30123/rest").readText())
    }
}

Also see Vaadin Boot: REST via Javalin.