The correct answer to this open question is the following.
The office in the US Treasury that manages the production of coins is the US Mint.
The US Mint is part of the Department of Treasure and is the one who can produce legal coinage in the United States. This office is authorized by the government to also produce any kind of commemorative coins or medals. The office manufactures and distributes precious metals, national medals, and collectible coins.
The office has six facilities along the United States and is located in Denver, Philadelphia, West Point, San Francisco, Washington D.C., and Fort Knox.