By default, JDK 11's HTTP Client supports cookies, but there are instances where built-in support is disabled. We can enable it as follows:

HttpClient client = HttpClient.newBuilder()
  .cookieHandler(new CookieManager())
  .build();

So, the HTTP Client API allows us to set a cookie handler using the HttpClient.Builder.cookieHandler() method. This method gets an argument of the CookieManager type.

The following solution sets CookieManager that doesn't accept cookies:

HttpClient client = HttpClient.newBuilder()
  .cookieHandler(new CookieManager(null, CookiePolicy.ACCEPT_NONE))
  .build();

For accepting cookies, set CookiePolicy to ALL (accept all cookies) or ACCEPT_ORIGINAL_SERVER (accept cookies only from the original server).

The following solutions accept all cookies and display them in the console (if any credentials are reported as invalid, then consider obtaining a new token from https://gorest.co.in/rest-console.html):

CookieManager cm = new CookieManager();
cm.setCookiePolicy(CookiePolicy.ACCEPT_ALL);

HttpClient client = HttpClient.newBuilder()
  .cookieHandler(cm)
  .build();

HttpRequest request = HttpRequest.newBuilder()
  .header("Authorization", 
          "Bearer mT8JNMyWCG0D7waCHkyxo0Hm80YBqelv5SBL")
  .uri(URI.create("https://gorest.co.in/public-api/users/1"))
  .build();

HttpResponse<String> response
  = client.send(request, HttpResponse.BodyHandlers.ofString());

System.out.println("Status code: " + response.statusCode());
System.out.println("
 Body: " + response.body());

CookieStore cookieStore = cm.getCookieStore();
System.out.println("
Cookies: " + cookieStore.getCookies());

Checking the set-cookie header can be done as follows:

Optional<String> setcookie 
  = response.headers().firstValue("set-cookie");