They vote for their parliaments and the EU parliament. Depending on national rules, the first nominates a commissioner, or they vote for an executive who does.

They vote for their parliaments and the EU parliament. Depending on national rules, the first nominates a commissioner, or they vote for an executive who does. The second has a veto. It's really no more removed than any US cabinet member, especially if you figure in the electoral college–yes, that's rather symbolic. But the difference to electing a parliament which elects the executive in the EU member state is still rather small.