The Commission is where legislation gets proposed, which then has to be approved by the Parliament and the Council. Neither the Commission nor Parliament can propose legislation themselves, but they can request that the Commission does so. To some extent, this is basically a safety feature to make sure the directives are properly written and do what they're supposed to. They can also amend proposed legislation (which would then need trilogue consultation between Parliament, the Commission, and the Council). Parliament also has the power to accept or reject a new Commission, and IIRC also to remove specific Commissioners.The be honest the Commision does not have a lot of power either. The real centre of power in the EU is the Council (The collective governments of the EU states.) That said it is somewhat opaque, and I would have to refresh my memory of who does what.
Amazing thing about getting old. You remember you used to know stuff but find that the details are often forgotten.
That said the parliament has a lot of power also.
A very rough comparison to the US would be that the Council is the Senate (particularly as originally designed where senators get appointed by state legislatures instead of by direct election), the Parliament is the House (where you have direct elections by the people), and the Commisson is the government – or at least the technocratic aspects of the government.