Buddy System V

If you truly have nothing better to do, go to the Dread Pit on a day when the story is Smashing Skardyn and it's bountiful. Jump into a tier 4 of it and run around stunning the Skardyn packs with the extra action button ability that Vanathia gives you at the start, and nuking them with some AoE. When they die, they explode and can damage other mobs around them, Nerubians included. Each Skardyn grants 10 or 11 Brann XP and there are 12-14 per pack with 11 packs throughout the delve. Along with picking up mislaid curiosities, you'll be looking at around 3235 Brann XP per clear, and the time a run takes depends on your class, speed stat, and iLvl. On my mage it takes about 3 minutes, on my less geared demon hunter it takes about 5. Lower level Brann's could definitely benefit greatly from this, however, the higher levels require 437,500 XP, so it's a wee bit slower..

I checked every difficulty and the Skardyn don't grant XP on T1-3, and they grant 10-11 on T4-7, and 13-14 on T8-11. Mislaid Curiosities also give the same XP regardless of difficulty, so T4 is the most efficient/easiest to farm. When you reach the end of the delve, just right click your portrait and leave delve and you can immediately walk back in to find your precious Skardyn alive and well and waiting for you.