The people who make the EU's laws in Brussels are not unelected bureaucrats; they are elected politicians, accountable to the people who elected them.
Virtually every law made in Brussels must be approved by two sets of democratically-elected politicians: the Council of the European Union, which is made up of government ministers from each member state, and the European Parliament, every member of which has been elected.
These are not unelected, unaccountable bureaucrats; they are elected, accountable politicians. (There may be occasional exceptions: the government of the UK, for example, includes 24 members who have not been elected by anyone - they are members of the House of Lords, unaccountable to anyone except the prime minister of the day. In any other country, the arrangement would be regarded as profoundly undemocratic.)