Korthite Crystals are a new material in Shadowlands Update 9.1 used to craft the Vestige of Origins, an optional crafting reagent that can increase the rank of any crafted legendary base item by two ranks. This means that players will want to farm Korthite crystals if they want to craft a Tier 5 or 6 legendary item. Shouldn't take you long to grab the 40 needed to create a Vestige of Origins, at least in theory.
Korthite Crystals in Shadowlands are obtained from the weekly Korthia event, Covenant Assaults, and Torghast Tormentors.
Korthite crystals have three guaranteed locations in Shadowlands: the weekly Korthia, Covenant Assaults, and the first Tormenters of Torghast event you complete in a week. Since you need 40 Korthite Crystals to craft the Vestige of Origins in Shadowlands, these three sources will only net you 4 total crystals per week (since Covenant Assaults are bi-weekly). This means you'll want to farm Korthia if you plan to avoid the exorbitant auction house prices, as you can see in the screenshot at the top of this guide.
Korthite crystals have a decent chance of spawning in hoards scattered around Korthia in Shadowlands. If you plan to cultivate Korthite crystals, you wanna hunt down all the treasures you can find. Additionally, Korthite crystals have a chance to drop as a reward from Korthia Daily Quests, so be sure to check in after each daily reset to see if the daily quests have any up for grabs.
Apart from these methods, well, you can always buy Korthite crystals from the auction house. If you want to craft the Vestige of Origins yourself, you will not only need 40 Korthite crystals, but also the help of a craftsman who knows the recipe (it can be purchased at Honored reputation from Death's Advance for 2000 Stygia). Only blacksmiths, jewelers, leatherworkers and tailors can make a remnant of the origins.
Once you have 40 Korthite Crystal and converted them into Vestige of Origins, you can then insert it into the optional reagent slot of any base legendary item you are about to craft for increase it by two rows. While high-end crafters and raiders with deeper pockets will aim for Tier 5 and 6 Legendaries as soon as possible, the poorer among us can instead farm our own Korthite crystals and use the Vestige of Origins to augmenting a slightly lower tier legendary base item, although that would arguably be a waste. All I'm saying is that the Vestige can be applied to any legendary base item rank, not just ranks 3 and 4. Do with this information what you want.
World of Warcraft: Shadowlands Patch 9.1, Chains of Domination will launch on June 29 (NA) and June 30 (EU).