Nowadays its easy to take for granted the large selection of blue pigments at our disposal. Several hundred years ago choices would have been more limited. Azurite was the cheapest and most available mineral source. It was for the same reasons I chose to make my first blue from azurite.
The color of azurite varies considerably, depending on how it is ground. When it is coarsely ground, like a fine sand, it is a very deep, royal blue. The finer it is ground, the paler it becomes. Painters could choose to take advantage of this quality. To make my pigment, I used the same levigation technique as I did with malachite. This would provide me with several different particle sizes.

The azurite as purchased. This was a nice sample. It was easily ground into a coarse powder.

I added the dilute egg yolk solution.

I decanted the mix a few times into separate bowls. The bottom bowl is leftover. The discolored gray appearance is due to impurities.

I poured off the rest of the liquid, removing most of the impurities. You can really see here how the color of azurite varies depending on how fine the grind is.
I repeated the refinement process several more times, regrinding the powder slightly finer each time.
Update: I was having some problems with the egg-yolk solution. Separating the finest particles from the leftover protein was difficult. I've switched from using egg yolk to a casein solution. I made a textbook tempera casein solution and let it sit overnight. The next day I highly diluted the mixture and then used it to levigate freshly ground azurite.

This change has allowed me to separate the smallest particles much more easily, with less waste. I was surprised by the beautiful new purity of color I was able to achieve.