Removing old rusty single hole faucet - please help!
The brass ring piece with the two holes in it is the part that needs to be removed. It should be able to be unthreaded from the tubing part that the hoses go up into.

Generally a special spanner wrench with two pegs on it would be used to turn the brass ring. The pegs would engage the two holes in the ring. Alternatively you could use an adjustable pliers or plumbers sink wrench to grasp the ring on its outer edge.