Activate Overgrown Estate by sacrificing Azorius Chancery.
When Azorius Chancery dies, Toph, Hardheaded Teach triggers, returning Azorius Chancery from your graveyard to the battlefield tapped.
When Azorius Chancery enters, it triggers, returning the artifact cast in step 1 from the battlefield to your hand, as it's a land due to Toph, the First Metalbender.
Resolve the Overgrown Estate ability
Repeat.
This clever loop turns your zero-mana artifact into an infinite recycling engine by layering land types and graveyard recursion. **Toph, the First Metalbender** acts as the crucial linchpin, turning your nontoken artifacts into lands so they can be targeted by bounce effects and earthbending. When you cast your artifact, **Toph, Hardheaded Teacher** triggers its earthbend ability to animate **Azorius Chancery**, which you can immediately sacrifice to **Overgrown Estate** to gain 3 life. Because **Azorius Chancery** was a creature and an earthbent land, its death triggers **Toph, Hardheaded Teacher** to bring it right back to the battlefield tapped. When **Azorius Chancery** enters, its own bounce trigger targets your artifact—now recognized as a land thanks to **Toph, the First Metalbender**—returning it to your hand so you can cast it all over again for infinite value, death triggers, and lifegain.