What happens if falling star kills honest broker and karthus at the same time?

Yes — Honest Broker's Deathknell triggers twice, so you get two Gold gear tokens, each entering exhausted.

Falling Star deals its 3 damage to both units in one resolution, so they die simultaneously in the same cleanup. Karthus's "Your [Deathknell] effects trigger an additional time" is a passive, not a triggered ability, so it stays active at the exact moment the Deathknell trigger is created — even though Karthus is dying in that same event (FAQ #12621; Rule 808.1.d). Honest Broker is controlled by the same player, so it's one of "your" Deathknell effects.

This is different from the Baited Hook line (FAQ #8551), where Karthus arrives from the trigger after the Deathknell was already created — there the doubling doesn't apply.