My house is only 2 years old and has begun making a "hammering" noise when I turn on the cold water tap in the bathroom only. The water will actually stop flowing in a moment or two.

I doubt the kitchen tap is actually turning itself on - or is it?
Perhaps fluctuations in water pressure are defeating the tap...

More details would have been helpful, such as mentioning the tap design (traditional or quarter turn type?) and when the hammering noise happens?

Hammering is often caused by a worn tap. When turned partly on the jumper can vibrate and cause the pressure in the pipe to fluctuate and magnify the noise, especially when there is a long run of pipe that is inadequately clipped to the wall...

Install air chamber to cushion sudden-stop of flowing water.
Water flow coming to sudden stop is called water hammer, and will bang pipes, but also loosen plumbing joints, causing leaks.
http://waterheatertimer.org/How-to-troubleshoot-electric-problems-with-water-heater.html#bang
http://waterheatertimer.org/images/Flow-rates-water-hammer-600.jpg

Air chamber has to be vertical, and about 18" long, with cap on top.
By code each Hot and Cold line at each tap will have air chamber located behind the wall. So there are two air chambers at each tap.

In your case, you can probably add air chamber to your Hot and Cold lines and solve problem for both dwellings.

Water hammer is caused because water does not compress like air.
So when long column of water suddenly stops... the whole pipe-full of water comes to sudden halt... and that water could weigh 1-1/2 pounds ... and just like a hammer head moving, the weight of water bangs the pipes to dissipate energy, causing noise.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

You have to install anti knock pipes into your plumbing, it's quite common. Go to the local home center you can by pre made or make your own as I did when remodeling my basins. Good Luck..

indicates that you have ceramic 1/4 or 1/2 turn inserts in the taps
These taps are very quick action taps and the water flowing is stopped immediately resulting in water hammer
The air chambers you have installed ( accumulators ) may be working but the pipes will suffer the water hammer all the way back to the utility tap on the foot path
Find out the utility pressure to the house and then you may have to install a pressure regulator on the inlet pipe to reduce that pressure to stop the water hammer

You have water hammer effect it is caused by a fast closing valve,it can be solved by installing a water hammer arestor in the plumbing line or maybe the water pressure is too high and a pressure reducing valve can be installed in the main water line.(the pipes in the wall are not secured properly that's why they vibrate)

Your washer has 2 seperate valves for hot and cold. Sounds like the hot water solenoid valve has failed.

no water hammers installed above the water heater. You can buy these hammers but they are not fun to put on yourself

Would you describe it as a popping or more like a knock sound? You may have a bad spring inside your compressor allowing the piston housing to contact the case wall of the compressor. It usually sounds like someone tapping a thick piece of steel with a hammer.
If the pop noise occurs well after the unit shuts down it may just be the liner has contracted from the cold and is shifting around, make sure it is not set too cold.

Sounds like you need to replace your shower valve, especially if this is the only fixture in the house being affected. You could try to replace the cold water cartridge first. Hope this helps

You are describing a problem known as water hammer. This will ultimately cause damage somewhere in your plumbing system so it should be addressed. If you are handy you can install an air chamber near the sink. If you want more information let me know. good luck.