After 2 PVA clogged BB cores, I learned my lesson about printing with wet PVA. Was using Ultimaker Natural PVA and even after several trips through the filament dryer, I could still hear some popping when it printed. Sure enough the BB Core clogged. No amount of hot pulls and heating the core helped.
Wanting a solution other than buying another BB Core, I decided to take one of my clogged cores apart. It was simple with a 7mm socket and a vise. The nozzle was blocked solid with burned PVA. I dropped the nozzle in a cup of water and over the course of 5 days finally got it clear. Took the nozzle out each day and dug at the hardened PVA with a dental pick. Bit by bit I was able to clear it.
Carefully reassembled and back in the printer. Worked like a champ. So, I decided to do the same thing with the second nozzle and this time took pictures to share. The PVA wasn't burned in this one like the original, but it still took 3 days of soaking and picking to get it clean. You can see here the nozzle in the vise, the clogged nozzle, and in the last photo all the crud that came out of it.
I've read here that you can't take the nozzle out of the BB Core, so wanted to share that although maybe it isn't the optimal approach, you can do it and reassemble successfully. With the cost of these cores, good to know that its at least worth a try when all else fails.