One way to do this is by using ECS awslogs log driver. AWS provide auto-configure option to create new log groups for this. See: https://docs.aws.amazon.com/AmazonECS/latest/developerguide/using_awslogs.html#create_awslogs_loggroups

Finally, we only need to configure our Laravel app to use LOG_CHANNEL=stderr. All logs will be collected and stored in CloudWatch.