A shopper in the United States opened a Cheddar that had been aged two years before sale and found hard white objects inside it. The complaint went back to the manufacturer, who dug the pieces out, the largest about five millimetres across, and sent them to the University of Vermont to be identified.
A powder x-ray diffractometer named them: calcium lactate pentahydrate, a crystal the cheese had grown inside itself while it aged. The same instrument, run over the small white specks in a two-year Parmigiano-Reggiano, found tyrosine, an amino acid, and only tyrosine.
That is what the crunch is, and it is not one substance. In the Italian wheel it is protein that ripening has pulled apart until an amino acid stops staying dissolved. In the Cheddar it is a different crystal with a different chemistry behind it.
National Cheese Lover's Day comes with no instructions attached. Working out what the white bits in a good aged wedge actually are is one of the better ways to spend it.