Customer there are numerous things that could cause your problem.
Honestly in my experience, the Edges are very trouble free vehicles. The one problem though is when there is a problem, it is a very complex to diagnose problem. I have seen a few with very odd electrical issues that have taken a lot of time to figure out. Unfortunately none of them have been stalling problems.
If I were working on it I would focus on three possibilities.
The first possibility would be a fuel pressure loss causing the stall. Fuel pumps can fail intermittantly causing stalling problems at times. The one problem I have with this theory is this. Usually fuel pumps will fail when they are hot. They may cool and restart, but it takes more than a minute. This is also usually a progressively worsening problem.
The second is a loss of engine computer function. There are no less than six computers in the Edge that are networked together to make sure everything is working well together. The antilock braking module tells the powertrain computer how fast the vehicle is moving so the powertrain computer knows when to shift. That is just one example of how they work together. If any one module on the network fails it can, depending on the failure, shut down the entire network and essentially shut the vehicle down. Even if the modules are ok, a sensor that is going bad can short out and shut the computer down and cause a very similar concern.
From there it could even be a loose wire in the network, power, or ground circuits that could cause intermittant issues with the modules and communication network.
If there is a network issue each module on the network will set codes stating the module cannot communicate with the other modules. Usually all the modules, except the one that is failing, will have these codes. The one that is shutting down usually does not know what is going on and will not set a code. From there you need to figure out if a sensor is going bad, a wire is loose, or the module itself is failing.
You could also have a throttle body problem. But these always cause a light to come on in the dash. A wrench light and check engine light. So, I highly doubt this is your problem.
If you talk to the dealer soon, ask them if they got any codes. If they did ask them for ALL of the codes make sure they tell you which codes are from which module. They should check all the modules for codes. If you get the codes send them to me. I may not be able to determine an exact cause, but I could possibly give you an idea of where to look.
Hope this helps, if you have any further questions do not hesitaet to ask.