The commissioners are chosen from the governments of the member states and then go through a complicated vetting and election process. To achieve such an indirect representative structure was actually one of the major goals of the UK together with other countries, in order to limit the power the EU has over individual governments.

Hence, this appointment system, which is additionally kept in check by the European Parliament whose members are elected directly by the voters from all member states.

You could complain that it's too representative, but not that it's not democratic. The alternative of giving the European Parliament more power and let it constitute a "European Government" directly has not been found appealing by the governments of its member states, particularly not by the UK, since they do not want to give away so much of their sovereignty.

Complaining about lack of democracy in the EU while at the same time complaining about lack of national sovereignty is perhaps the most hypocritical and intentionally misleading part of the current populist agenda.

Keep in mind the European Commission is chosen largely by the heads of state of the various EU countries, and must be approved (and can be dismissed by) the european parliment. The EU parliment has most of the power and is democratically elected.

The Commission cannot create law alone and undemocratically.

The European Commission drafts legislation and then the European Parliament decides whether or not to amend or pass the legislation.