Too much gas and my car "chokes"/dies

2001 Audi A4 ~140K When I fill up the gas tank until the gas pump handle clicks off, my car will “choke”, cough, sputter and die at intersections for the first 50 miles if the car is hot. If I fill up and only do little short trips less that 2-3 miles for the first 50 miles, it is fine. If I fill up and drive more than 2 or 3 miles, it will do this. This started at the beginning of summer. What I’ve been doing to negate this problem is I only put in $40 worth of gas so that the tank is a few gallons short of truly full and it hasn’t done it.
What is this crazy problem?