public class LabelServlet extends SimpleAsyncJpaServlet {

    @Inject MyDao dao;

    @Override
    protected void doPost(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {
        // this code will be executed on the app wide executor associated with persistent unit,
        // so threads from server's main thread pool will not be waiting on JPA operations
        // nor for JDBC connections to become available.
        try (
            PrintWriter writer = response.getWriter();
        ) {
            MyEntity myEntity = dao.find(Long.valueOf(request.getParameter("objectId")));
            for (String label: myEntity.getLabels()) writer.println(label);
            String newLabel = request.getParameter("newLabel");
            if (newLabel == null) return;
            performInTx(() -> {
                myEntity.addLabel();
                writer.println(newLabel);
            });
        } catch (Exception e) {
            throw new ServletException(e);
        }
    }
}

@WebListener
public class ServletContextListener extends JpaServletContextListener {

    @Override
    protected String getMainPersistenceUnitName() {
        return "my-persistence-unit";  // same as in persistence.xml
    }

    @Override
    protected int getMainJpaThreadPoolSize() {
        // return the same value as my-persistence-unit's connection pool size. This way threads
        // from the pool will never have to wait for a JDBC connection to become available
        return 10;
    }

    @Override
    protected LinkedList<Module> configureInjections() {
        var modules = super.configureInjections();
        modules.add((binder) -> {
            binder.bind(MyDao.class).to(MyJpaDao.class).in(Scopes.SINGLETON);
            // more bindings here...
        });
        return modules;
    }

    @Override
    protected void configureServletsFiltersEndpoints() throws ServletException {
        addServlet("label", LabelServlet.class, "/label");  // will have its fields injected
        // more servlets/filters here...
    }
}

public class MyJpaDao implements MyDao {

    @Inject Provider<EntityManager> entityManagerProvider;

    @Override
    public MyEntity find(long id) {
        return entityManagerProvider.get().find(MyEntity.class, id);
    }

    // more dao stuff here...
}