I assume the yolks are not quite dry enough? I would shell them, break them up a bit and microwave for a few seconds or whatever it takes. Once cooled mash them up for egg salad.

You could make tea eggs - gently crack but don't remove the shells then simmer gently in tea (maybe a smoky tea) then when you peel them they are infused with flavor and look like marble. Or you could peel them then simmer them very gently in dashi or flavorful broth and get a hard boiled version of the eggs that you get with ramen. Depending HOW underdone they are, they'd probably make an excellent egg salad too!