Slightly different approach:
MultiValueMap<String, String> headers = new LinkedMultiValueMap<String, String>();
headers.add("HeaderName", "value");
headers.add("Content-Type", "application/json");
RestTemplate restTemplate = new RestTemplate();
restTemplate.getMessageConverters().add(new MappingJackson2HttpMessageConverter());
HttpEntity<ObjectToPass> request = new HttpEntity<ObjectToPass>(objectToPass, headers);
restTemplate.postForObject(url, request, ClassWhateverYourControllerReturns.class);