Oftentimes I want to call a promise and just let it run asynchronously instead of waiting for it. Like:
... some code ...
fetchMyCount().then(count => {
Exactly for issues like this, I wrote my own utility for writing asynchronous code:
https://github.com/vacuumlabs/yacol/
It does not help you with your existing code, however with newly written code it provides (among many other things) quite advanced error-handling capabilities.
This said, I don't think that "unhandledRejection" / "uncaughtException" events are good (although it's the best node.js natively provides) tools to do proper error handling:
First, you can only attach it process-wide, so it forces you to handle all uncaught errors the same way (unlike with try-catch where you can react differently to errors that originate from different parts of your code)
Second, "unhandledRejection" is called if .catch is not attached to the Promise in the same run of event loop. This may result in false errors being caught; note it is pretty OK to attach error handler to the promise later!