What was the name of the united nations body the general assembly created specifically to supervise all nuclear energy production?

The United Nations Atomic Energy CommissionExplanation:

Nuclear concerns were paramount for the United Nations from its very beginning.  Resolution 1 of the United Nations General Assembly (January 24, 1946) established the UN Atomic Energy Commission to make specific proposals:

(a) for extending between all nations the exchange of basic scientific information for peaceful ends; (b) for control of atomic energy to the extent necessary to ensure its use only for peaceful purposes; (c) for the elimination from national armaments of atomic weapons and of all other major weapons adaptable to mass destruction; (d) for effective safeguards by way of inspection and other means to protect complying States against the hazards of violations and evasions.   (UN General Assembly, Session 1, Resolution 1)

A further group was established by the UN General Assembly in 1956.  The International Atomic Energy Agency (IAEA) was established with these goals, as outlined in the statute endorsed by the UN General Assembly:

The Agency shall seek to accelerate and enlarge the contribution of atomic energy to peace, health and prosperity throughout the world. It shall ensure, so far as it is able, that assistance provided by it or at its request or under its supervision or control is not used in such a way as to further any military purpose.