What exactly is overly bureaucratic in the EU?

I as an European get the feeling people usually hate on the EU just because it dares to interfere with local legislation. But that's its job. And usually the EU interferes for a good reason. Usually because member countries falling back to only thinking about themselves and forgetting that we Europeans are in this shit together.

> you can't do that

It's good that you can't call sparkling wine that's not from the Champagne "Champagne". It's good that you can't screw over flight passengers the way they do in the US. It's good that you can't annoy customers with phone power sockets that change with every model.

When I hear about actual examples of excess bureaucracy, it's usually on the country-level.

When people talk about the EU, they don't necessarily mean the EU proper, just like many "US" problems are more at the state or local level. People often mean "within the EU", including national regulations that may be widespread.