If I use Baited Hook on Honest Broker and I play Karthus off of the trigger, how many times does Honest Broker's Deathknell trigger?

Honest Broker’s Deathknell will trigger one time.

According to the official FAQ regarding the interaction between Baited Hook and Karthus, Karthus must be on the board at the moment the Deathknell trigger is created for his doubling effect to apply.

Sequence of Resolution:

1. Baited Hook resolves: You kill Honest Broker.
2. The Deathknell trigger for Honest Broker becomes pending. It cannot enter the chain yet because Baited Hook is still resolving (Rule 734.1.d.2).
3. Baited Hook continues: You look at the top 5 cards and find Karthus, Eternal. Karthus is played and becomes a pending item on the chain.
4. Baited Hook finishes resolving. Now, all pending items finalize in the order they were created:
   • First, the Deathknell trigger finalizes and enters the chain.
   • Second, Karthus finalizes and resolves immediately (as a unit permanent), entering the board.
5. Because the Deathknell trigger was already created and put on the chain before Karthus was on the board, Karthus's passive ability ("Your Deathknell effects trigger an additional time") does not see the event to double it.

Summary: Karthus needs to be on the board when the trigger happens, not just when it resolves. Since Honest Broker died while Karthus was still in your deck/pending, you only get the single trigger.