Cross region lambda setup

I am trying to setup a lambda in one region that will get ec2 running events from a few different regions (all regions are in the same account).

I tried 2 different ways. I found that in Event Bridge in us-west-2 I was able to create a rule for the ec2 running event and tell it to send the event to the default event bus in us-east-1 (where my lambda is). So I tried this and looked at the logs but I see no logs nor am I seeing the lambda run.

Then I tried to create a SNS topic in us-west-2 for this. I pointed the Event Bridge rule to the SNS topic and added the SNS topic to the lambda in us-east-1. Again I am not seeing any logs for this nor am I seeing that the lambda ran.

Are there any good tutorials on how to set this up?