I have two bathroom sinks his/hers, same vanity, about 6 ft. apart horizontally. One drains fine, the other is "weird". Both go into the exterior wall, each with it's own 1.5" pvc fitting at the wall, in line with the sink center, with slip joint 1.5" thin wall pipe from the wall to the bowls, identical in every way. The wall fittings are at the same elevation, about 10 to 12 in. below the bottom of the identical bowls. Standard p traps on both.
If the "problem" sink is filled partially, less than 1/2 or so (about 3 to 4 in.), it takes 5 to 8 minutes to drain. The other good sink drains the same amount in 5 seconds or so. So, you might think obstruction, but: When the problem sink is filled mostly full, about 8+ inches, it drains just fine... all the way to the bottom. Seems like a siphon effect is helping it. I first replaced the entire thin wall under the vanity, new "P" trap, new drain in the sink. No good. Then added an indoor "air admittance" vent with standpipe on the dirty side of the "P" trap, thinking venting was the problem. There was no change. I have not tried snake, etc, since the sink does drain right when full, and therefore does not seem to be obstructed. I'm only left with the notion that the run in the wall may be slightly uphill to the point where the two drains meet. I can't get to that without tearing out the vanity and sheetrock.
The problem has always been that way since we got the house 2 years ago. It is 15 years old. All other drains in the two-bath home are fine. All are on same level, and the home is concrete slab built, community sewer. Don't know if the problem was there from time zero, but it has not changed (+or -) for the two years we have owned it. Any ideas?

Perhaps this should be under "Paranormal Phenomenon"?

A non-plumber thought would be that the extra initial force of the mass of water in the full slow sink is able to push a moveable obstruction out of the way that otherwise inhibits the lower flow when the sink isn't full.

Have you tried plunging it?

Then added an indoor "air admittance" vent with standpipe on the dirty side of the "P" trap, thinking venting was the problem. There was no change.
If the "dirty side" of the trap is before the trap then you installed it on the wrong side, (see image). Regards, Tom

I think they call the dirty side, the side with the sewer gas(after trap). So I am prettysure they installed it right.