"You being an Asian does not / don't know this"

Solution 1:

It may become more apparent if you move the 'you' to the other side of 'being an Asian,' making the sentence:

It's a shame that, being an Asian, you does not know this.

'You does' should become 'you do,' making the sentence:

It's a shame that, being an Asian, you do not know this."

Solution 2:

No. I think you want:

"it's a shame that you, being (an) Asian, do not (/don't) know this"

Solution 3:

Instead of 'being an Asian', the term 'as an Asian' might work well.

It’s a shame that as an Asian, you do not know this.

You'd probably be better off totally rearranging the sentence to make it clearer.

It's a shame that an Asian like you does not know this.

or

It's a shame that an Asian such as you does not know this.