My 2001 V11 has been going through the same problems. Ride, stop, a short time later, try to start, stalls, let it cool, runs fine. I posted on this problem a few months ago. I had an interesting conversation with a tech at Harpers MG who said vapor lock can be a problem with our 2000-2001 V11s given the location of the fuel pump, right over the center of the motor. He said this problem was dealt with by Guzzi when they moved the fuel pump forward in the 2002+ V11s. He said he can send me the mounting clamps for the 2002 V11 fuel pumps and extended fuel line which would fix the problem. For what it is worth, my fuel pump is on the bottom of the backbone, with the filter on the top.
Does any one have experience with this fix?