From: https://www.fungusfactfriday.com/119-pisolithus-arrhizus/

The Dyeball, as its common name implies, can also be used for dyeing wool. P. arrhizus is counted among the best mushrooms for dyeing and imparts wool with a deep brown to reddish-brown to blackish color. The pigments come from the tar-like gel between the peridioles, so younger Dyeballs work better.

This may also be of interest to you, even though they do not use this specific mushroom: https://www.youtube.com/watch?v=T4TjnxFO3yw

It's a dyeball (Pisolithus arhizus).

Everyone was pretty close.