Given plain text of given cipher text, can AES key be uncovered? How difficult is it to find the AES key if attacker has IV and ciphertext of a known plain text?

I am assuming 128 bit key size.
It is not possible to find an AES key from a known plaintext / ciphertext pair. If that was the case then AES would either have to be:


vulnerable with regard to the key size or;
vulnerable against attacks that invalidate the cipher.


AES has a security close to the key size (of 128 bits, in your question). Brute force or more intricate attacks against the key itself are therefore infeasible.

And, as indicated by the text above, the cipher has certainly not been broken in a sense that you can (easily) recalculate the key. Allowing an attacker to find the full key is as broken as a cipher can get; in general it is assumed that an attacker knows parts of the plaintext.

The mode of operation and IV are inconsequential to the security of the key as the key is only used as input of the block cipher - both in CBC and GCM mode. The key is therefore protected by the block cipher itself.