Not sure anybody has suggested that the EU has invaded anywhere. Yes, countries choose to join, but once joined if they become unhappy and unable to change things, the wanting to leave has the effect not dissimilar to independence from a colonial power. Triggering Article 50 seemed like starting the fourth chimurenga
The EU in itself may not have invaded, but most of the Western Europe members have previously invaded, took over, colonised, and in some instances carved up the land by drawing straight lines on the map. Below is the notable ones - the list is not exhaustive:
Great Britain - Ireland, North America, parts of Africa, parts of Asia, Caribbean, South Pacific, Gibraltar, Malta, Cyprus, Australia
France - Parts of Africa (including the Congo Brazzaville), South Pacific, Polynesia, Quebec in present day Canada
Denmark - Faroe Isles, Greenland
Belgium - they even had a go themselves in taking over the Congo (Leopoldsville), which eventually became Zaire before reverting to DR Congo
Netherlands - Parts of Caribbean islands, West Indies
Italy - the Venetian Empire took over Slovenia, Roman Empire worked northwards into Great Britain as far north as the Antonine Wall
Spain - Much of Central and South America, California, parts of North Africa, Cuba
Portugal - Brazil, Mozambique, Angola, the Goa region in India
Austria and Hungary - Slovenia, parts of the Balkans, parts of Czechoslovakia and Poland
Germany - parts of Western and Eastern Europe mainland. Hitler attempted to push his luck by trying to take over Russia and oust Stalin
As can be seen above, most of Western Europe has done a fair amount of invading and taking over in terms of imperialism and empire building.