Bluetooth Receiver HSP

Greetings, I have a pair of Bose QuietConnect 35 ii. I need to build a receiver for these that support the HSP profile and A2DP profile. The receiver would then break out the “audio playback” and “microphone” to go to the aux input and mic input of an old computer (I can’t add a bluetooth receiver directly, such as USB receiver, etc.).

Is such a critter possible?