Appropriate word for someone immune to embarrassment?

I am looking for a word which can be used to describe someone who is very "comfortable in their skin", secure with themselves, and most importantly completely immune to being embarrassed or mocked.

Some examples might include consistently mispronouncing a word in a conversation (like "pirate" instead of "pilot") without feeling silly, even though others try to mock him/her. Or more seriously, not feeling embarrassed at all if their private photographs (ie in the shower or some other scandal-like situation) were leaked.

Words like "unashamed", "unabashed" or "unapologetic" usually have a negative connotation and do not seem applicable, since the person is not necessarily doing things which society would consider shameful from a moral standpoint.


unflappable

adjective

  1. not easily upset or confused, especially in a crisis; imperturbable.

dictionary.com

I like this word better than imperturbable for the idea of being cool and collected, even in the face of intentional attempts to embarrass or harass.


I'd suggest:

thick-skinned

adjective

  1. insensitive or hardened to criticism, reproach, rebuff, etc

dictionary.com

It may be because I come from East Asia but this is the phrase I most often hear (the phrase also exist in Malay and I believe Mandarin).

It does have a slight negative connotation but I honestly don't believe there can be any word or phrase about the concept of someone not listening to criticism that can get away from any negative connotation. Even words like "brazen" imply that the person is overconfident.


I don’t fully understand the question and its constraints, so I’ll naïvely suggest the obvious shameless.  But, if you want something value-neutral, and you don’t like imperturbable (suggested by another answer), then possibly composed might work:

calm and in control of your emotions