If you are doing the Anniversary Event that happens around April of every year (2024 link here), any daily or weekly quest you complete will earn you an Anniversary Gift Box (in addition to their regular rewards).
These reward boxes contain crafting materials (ore, ingredients, runes, etc.) and a single rare crafting item (Nirncrux, style items, motif pages, etc.)
The best and fastest way to farm Anniversary Boxes is do Crafting Writs. Other methods will take you much longer just to earn a single box.
Doing six writs at one go nets you six anniversary boxes!
Plus, you should do this on every character you have – use up all 8 character slots and level each of them up to Level 6 to do writs before the event starts.
And yes, you can achieve it with these add-ons
You’ll need the primary mats (materials) such as Jute, Sanded Maple and Rawhide. They’re fairly easy to come by except for Jute. Stock them up before the event starts!
EXTRA TIP: Do the dailies on the day before the event starts but only submit them AFTER the event starts!
EVEN EXTRA TIP: Do the writs in Vivec City (Vvardenfell). ALL the crafting stations and writ submission point are close to one another! No doors and even the bank/merchants are easily accessible
Southern Elsweyr DRAGONS (Next BEST)
Alternate best for unlimited boxes. Dragons spawn one after another in different locations.
And you only need to hit it once (unlike Dolmens where only the top DPSers get loot). About one box for every 3 minutes depending on crowd DPS. Note, healing others does not count as DPS.
During peak hours, you must hurry and score at least 1 hit on the dragon before it dies to get loot. You may also want to tone down your video settings due to the number of players that may overtax your card.
For more (slower) quests, see here