There's no tool, technological or legal, to block/ban a website EU-wide.

They banned Russia Today EU-wide.

The EU can declare a company a criminal enterprise and the financial industry must then prevent EU citizens from transacting with them.

They said blocking a website

They will set their DNS servers to drop all incoming connections to X. That can be done in each country. They can use Deep Packet inspection tools and go from there. If the decision is EU wide then they will roll that out.

Deep packet inspection? What do you mean? Are you talking about domain name confiscation or building a Great Firewall of EU?

The EU has DNS servers?

The DNS servers take incoming connections to anything other than the DNS servers?

The EU has deep packet inspection tools?

There is no law that would permit the EU to do this. This would be a huge thing to introduce and implement, probably a 2-3 year project, and would almost certainly be strongly opposed by multiple member countries.