Cut and paste from Wikipedia:
There is one member per member state, but members are bound by their oath of office to represent the general interest of the EU as a whole rather than their home state.[3] The Commission President (currently Ursula von der Leyen) is proposed by the European Council[4] (the 27 heads of state) and elected by the European Parliament.[5] The Council of the European Union (informally known as the Council of Ministers) then nominates the other members of the Commission in agreement with the nominated President, and the 27 members as a team are then subject to a vote of approval by the European Parliament.[6] The current Commission is the Von der Leyen Commission, which took office in December 2019, following the European Parliament elections in May of the same year.
There is another section on Council of the European Parliament.
Not sure how you conclude this is undemocratic, I find the US, with voting maps re-drawing, popular votes, electorates and so on to be far more undemocratic, if democracy is assumed to mean that each person under the rule has an equal say.