Here is how we do it. Your beloved EU which wants to get so involved sets up it's own voluntary armed force. Let's calll it the EUVF as it has a nice ring about it. It then asks for volunteers from it's member states who are EU citizens to join. They could even ask further afield if they want and welcome others. Remember those jets they are supplying, well it purchases them and other military kit for nominal sums from it's member states- say a grand a jet. It then badges them with a blue roundel with yellow stars on them and bases them in western Ukraine. They then set about the Russians. The Russians can't hit them back as a country as they aren't one and NATO aren't involved. If the Russians attack one of the EU member states which is a Nato member then in we all pile in including the UK and US. At the end of the conflict it sells the kit back to the relevant parties for the same price.
There you go. The EU also become a major player which is what they want