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"cabinet members are nominated by the president and approved by the Senate. The European Council, which is essentially the EU’s chief executive body, comprises the 28 member countries’ leaders, all democratically elected. Its president, Donald Tusk, is elected by those leaders rather than directly by voters"
Good article to provide to the thread Danny.
So how i see it, they are elected, and we influence that by who we vote for at council level to make people a Member of Parliament of the United Kingdom