A few things to address ...
Don't put HttpServletResponse and PrintWriter as field members.
Keep in mind that you have 1 instance and multiple requests.
Don't call baseRequest.setHandled(true) till you are done handling the request.
Don't forget to close your writer.
Using the try-with-resources pattern that might make this easier for you (as PrintWriter is an AutoCloseable resource)
try(PrintWriter writer = response.getWriter())
{
// your logic on what content to respond with.
writer.println("Hello");
} finally {
baseRequest.setHandled(true)
}
Under Jetty, you can have multiple handlers work with the same response.getWriter(), merely ending the handler, or setting the baseRequest.setHandled(true) is not sufficient to let jetty know that the response is done.
If you don't want to close the PrintWriter, at least flush it. (but know that an unclosed Writer will result in Jetty issuing the response content as chunked)
(Note: the Handler behavior in this regard is different than the Servlet behavior)