would give your eye teeth
give (one's) eye teeth for (something)
To give or relinquish anything (or something very valuable) in order to receive some specific thing in return. Oh, I would give my eye teeth for curly hair like yours.
would give your eye teethBRITISH, INFORMAL
If you would give your eye teeth for something or to do something, you would love to have or do that thing. He's the most exciting man I've ever worked with, and I'd give my eye teeth to do something with him again. I'd give my eye teeth for an opportunity to join that company. Note: A person's eye teeth are their canine teeth, the pointed teeth near the front of their mouth.