Whenever I use the warm or hot water settings on my new washing machine, it makes a hammering noise unless I turn on the COLD water on the utility sink next to it.

Why does this happen & how do I stop it?

Your new washer probably has a better fill valve that shuts off quickly causing water hammer. You can install water hammer arrestors near the shut off valves for the washer. They aren't too expensive and some new versions do not require soldiering.