Activate Troubled Healer by sacrificing Izzet Boilerworks.
When Izzet Boilerworks dies, Toph, Hardheaded Teach triggers, returning Izzet Boilerworks from your graveyard to the battlefield tapped.
When Izzet Boilerworks 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 Troubled Healer ability
Repeat.
This ingenious loop transforms ordinary artifacts into a renewable resource, turning your mana base into an engine of endless triggers. Thanks to Toph, the First Metalbender, your nontoken artifacts are treated as lands, allowing Troubled Healer to happily sacrifice them. When you cast a zero-mana artifact, Toph, Hardheaded Teacher triggers to earthbend your Izzet Boilerworks into a creature. You then sacrifice that land-creature to Troubled Healer to trigger its damage prevention. The brilliant safety net of Toph, Hardheaded Teacher's earthbend ability immediately returns Izzet Boilerworks to the battlefield tapped upon its "death." When Izzet Boilerworks enters, its own bounce trigger forces you to return your artifact-land back to your hand, ready to be recast for free all over again.