@Travis Troyer Thanks for reaching out.
It seems like you are looking for a way to capture and log exceptions that are caught by the Azure Function host in Splunk. While Azure Functions integrates with Application Insights to collect telemetry data, it does not provide a built-in way to route exceptions to Splunk. However, there are a few options you can consider to achieve this.
One option is to use Azure Monitor Logs to consolidate logs from different resources, including Azure Functions, in the same workspace. You can then stream your logs and events to a Logs Analytics workspace and connect Microsoft Sentinel to this workspace for enterprise-level threat detection and response automation. You can learn more about this in the Monitoring Azure Functions with Azure Monitor Logs article.
Another option is to use Azure Functions' built-in logging feature to log exceptions to a file or to a third-party logging service such as Serilog or NLog. You can then configure Splunk to monitor the log files or the logging service to capture the exceptions. You can learn more about this in the Analyze Azure Functions telemetry in Application Insights article.
If you decide to use a third-party logging service, you can use the logging framework of your choice, such as ASP.NET Core's ILogger or Serilog's ILogger, to capture and log exceptions. You can then configure the logging service to send the logs to Splunk.