It could be an off flavor from a mild contamination. Some molds can give a sense of dustiness.
Also, going off what dmtaylor said:
dmtaylor wrote:It sounds like the OP might be describing a husky, perhaps astringent flavor. Could be from over-milling the grains, or bad mash pH, possibly. Assuming it's not the biscuit, which is still our first guess.
When I try and drink my beers before they are ready sometimes they have an intense husky grain flavor like when you chew on raw malt and I could see that being described as dusty. If it's that all you need to do is let it cold condition longer. It's probably caused by a polyphenol that coagulates and settles out.
If it's astringent like oversteeped tea or like a very tannic red wine then you extracted tannins in the mash.