Water worked fine up until about two weeks ago.

Kitchen faucet is two handle Moen. House is 30 years old but kitchen
remodeled about a year ago. Copper water pipes throughout house.

Have GE dual filter water filtration system tapped into the cold water
line with separate faucet for the filtered water mounted to sink.

Filters changed about 3 months ago (6 month lifecycle)

Everything worked fine until about two weeks ago when we noticed
that when we turn on the cold water, it would run fine for about 10-15
seconds, then there would be a "clunk" in the line and the water would
almost come to a complete stop (just a trickle of water coming out of
the faucet).

If we turn the handle off, wait about 5 seconds and turn it back on,
the water will again flow fine for about 10-15 secs then repeat the
same problem with cutting off.

Same thing will happen if we just use the water filter faucet.
However, if we turn *both* the filter faucet and cold water on at the
same time, water will cut off to both in about 3-4 seconds.

Meanwhile, the hot water side works fine.

Cutting off the water line to the filter (it has a cutoff where it's
tapped into the cold water line), has no effect. The cold water
will still shut off with a clunk after 10-15 seconds.

No other water lines in the house has this problem.

Any ideas what may be causing this?