For some reason I can only repro this from Dart Code, not from the command line/Observatory... However I don't believe there's anything obviously wrong in VS Code.
I'm running a small sample app on flutter-tester and it breaks at startup on this:

However if I go up the stack to OptionalMethodChannel.invokeMethod there is a catch statement that would catch this exception:

I've confirmed that exception pause mode is Unhandled:
[14:31:12]: ==> {"id":"5","method":"setExceptionPauseMode","params":{"isolateId":"isolates/1027928886","mode":"Unhandled"}}
Here are full logs from Flutter Run + Observatory: